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Algebra Word Problems
Lesson 6
Worksheet 6
Algebra Word Problems
Involving
Speed, Distance and Time
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Algebra Word Problems – Lesson 6 - Worksheet 6 - Algebra Word Problems
Involving Speed, Distance and Time
Problem 1) Two planes leave an airport and fly in opposite directions. One
plane flies at miles/hour and the other plane flies at miles per hour. How
many hours will it take for the two planes to be miles apart?
Problem 2) Two people leave from two towns that are miles apart and
travel toward each other along the same road. Person A drives miles/hour
(mph) slower than person B. If they meet in hours, at what speed did each
person travel?
Problem 3) Two people ride their bikes from the same place in opposite
directions. If they leave at the same time and person A rides times as fast as
person B, and after hours, they are miles apart, what are their cycling
speeds?
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Problem 4) Suppose you ride a bicycle to a store at a speed of miles/hour.
You then walk home at a speed of miles/hour. The total round trip time is
hours. How far from your starting point is the store?
Problem 5) Suppose you leave your house by bicycle and travel miles per
hour. One hour later, your brother leaves and travels down the same road by car
at miles per hour. How long, in hours to the nearest tenth, does it take for the
car to overtake the bicycle?
Problem 6) Two planes leave an airport and fly in opposite directions. One
plane flies at miles/hour and the other plane flies at miles per hour. How
many hours will it take for the two planes to be miles apart?
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Problem 7) Two people leave from two towns that are miles apart and
travel toward each other along the same road. Person A drives miles/hour
(mph) slower than person B. If they meet in hours, at what speed did each
person travel?
Problem 8) Two people walk from the same place in opposite directions. If
they leave at the same time and one person A walks times as fast as person B,
and in hours, they are miles apart, what are their walking speeds?
Problem 9) Suppose you ride a bicycle to a store at a speed of miles/hour.
You then walk home at a speed of miles/hour. The total round trip time is
hours. How far from your starting point, in miles, is the store?
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Problem 10) Suppose you leave your house by bicycle and travel miles per
hour. One hour later, your brother leaves and travels down the same road by car
at miles per hour. How long, in hours to the nearest tenth, does it take for the
car to overtake the bicycle?
Problem 11) Two planes leave an airport and fly in opposite directions. One
plane flies at miles/hour and the other plane flies at miles per hour. How
many hours will it take for the two planes to be miles apart?
Problem 12) Two people leave from two towns that are miles apart and
travel toward each other along the same road. Person A drives miles/hour
slower than person B. If they meet in hours, at what speed did each person
travel?
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Problem 13) Two people drove their cars from the same place in opposite
directions. If they leave at the same time and person A drives times as fast as
person B, and in hours, they are miles apart, what are their driving speeds?
Problem 14) Suppose you ride a bicycle to a store at a speed of miles/hour.
You then walk home at a speed of miles/hour. The total round trip time is
hours. How far from your starting point is the store?
Problem 15) Suppose you leave your house by bicycle and travel miles per
hour. One hour later, your brother leaves and travels down the same road by car
at miles per hour. How long, in hours to the nearest tenth, does it take for the
car to overtake the bicycle?
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Problem 16) Two planes leave an airport and fly in opposite directions. One
plane flies at miles/hour and the other plane flies at miles per hour. How
many hours will it take for the two planes to be miles apart?
Problem 17) Two people leave from two towns that are miles apart and
travel toward each other along the same road. Person A drives miles/hour
(mph) slower than person B. If they meet in hours, at what speed did each
person travel?
Problem 18) Two people ride their bikes from the same place in opposite
directions. If they leave at the same time and person A rides times as fast as
person B, and in hours, they are miles apart, what are their riding speeds?
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Problem 19) Suppose you ride a bicycle to a store at a speed of miles/hour.
You then walk home at a speed of miles/hour. The total round trip time is
hours. How far from your starting point, in miles to the nearest two decimals, is
the store?
Problem 20) Suppose you leave your house by bicycle and travel miles per
hour. One hour later, your brother leaves and travels down the same road by car
at miles per hour. How long, in hours to the nearest tenth, does it take for the
car to overtake the bicycle?
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Answers - Algebra Word Problems – Lesson 6 - Worksheet 6 - Algebra Word
Problems Involving Speed, Distance and Time
Problem 1) Two planes leave an airport and fly in opposite directions. One
plane flies at miles/hour and the other plane flies at miles per hour. How
many hours will it take for the two planes to be miles apart?
Solution:
Let represent the number of hours. Write and solve the following equation:
Answer: hours
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Problem 2) Two people leave from two towns that are miles apart and
travel toward each other along the same road. Person A drives miles/hour
(mph) slower than person B. If they meet in hours, at what speed did each
person travel?
Solution:
Using the variable as the speed of each person, we can write and solve
following equation for the speed of person B:
Person B’s speed:
Person A’s speed:
Answer: Person A’s speed: mph; Person B’s speed: mph
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Problem 3) Two people ride their bikes from the same place in opposite
directions. If they leave at the same time and person A rides times as fast as
person B, and in hours, they are miles apart, what are their cycling speeds?
Solution:
From the problem, variable represents the first person and variable
represents the second person. We can write and solve the following equations:
Since , substitute for in the second equation and solve for :
Use to solve for
Answer: Person A rode mph; Person B rode mph
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Problem 4) Suppose you ride a bicycle to a store at a speed of miles/hour.
You then walk home at a speed of miles/hour. The total round trip time is
hours. How far from your starting point, in miles to the nearest two decimals, is
the store?
Solution:
Let represent time in hours, represent the speed and represent the total
distance. We know that the following formulas apply:
Substitute the values from the problem into the second formula:
Multiply the equation by :
Answer: miles
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Problem 5) Suppose you leave your house by bicycle and travel miles per
hour. One hour later, your brother leaves and travels down the same road by car
at miles per hour. How long, in hours to the nearest hundredth, does it take
for the car to overtake the bicycle?
Solution:
When the car overtakes the bicycle, the distances each travel are the same. Thus,
we can use the formula, where is the distance, is the time, is the bicycle and
is the car:
.
Substitute the numbers from the problem into the formula:
Answer: hours
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Problem 6) Two planes leave an airport and fly in opposite directions. One
plane flies at miles/hour and the other plane flies at miles per hour. How
many hours will it take for the two planes to be miles apart?
Solution:
Let represent the number of hours. Write and solve the following equation:
Answer: hours
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Problem 7) Two people leave from two towns that are miles apart and
travel toward each other along the same road. Person A drives miles/hour
(mph) slower than person B. If they meet in hours, at what speed did each
person travel?
Solution:
Using the variable as the speed of person B and
as the speed of person
A, we can write and solve following equation:
Person B’s speed:
Person A’s speed:
Answer: Person A’s speed: mph; Person B’s speed: mph
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Problem 8) Two people walk from the same place in opposite directions. If
they leave at the same time and person A walks times as fast as person B, and
in hours, they are miles apart, what are their walking speeds?
Solution:
From the problem, variable represents the first person and variable
represents the second person. We can write and solve the following equations:
Since , substitute for in the second equation and solve for :
Use to solve for
Answer: Person A walked mph; Person B walked mph
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Problem 9) Suppose you ride a bicycle to a store at a speed of miles/hour.
You then walk home at a speed of miles/hour. The total round trip time is
hours. How far from your starting point is the store?
Solution:
Let represent time in hours, represent the speed and represent the distance.
We know that the following formulas apply:
Substitute the values from the problem into the second formula:
Multiply the equation by :
Answer:
miles
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Problem 10) Suppose you leave your house by bicycle and travel miles per
hour. One hour later, your brother leaves and travels down the same road by car
at miles per hour. How long, in hours to the nearest hundredth, does it take
for the car to overtake the bicycle?
Solution:
When the car overtakes the bicycle, the distances each person has travelled is the
same. Thus we can use the formula, where is the distance, is the time, is the
bicycle and is the car:
.
Substitute the numbers from the problem into the formula:
Answer: hours
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Problem 11) Two planes leave an airport and fly in opposite directions. One
plane flies at miles/hour and the other plane flies at miles per hour. How
many hours will it take for the two planes to be miles apart?
Solution:
Let represent the number of hours. Write and solve the following equation:
Answer: hours
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Problem 12) Two people leave from two towns that are miles apart and
travel toward each other along the same road. Person A drives miles/hour
slower than person B. If they meet in hours, at what speed did each person
travel?
Solution:
Using the variable as the speed of person B and
as the speed of person
A we can write and solve following equation:
Person B’s speed:
Person A’s speed:
Answer: Person A’s speed: mph; Person B’s speed: mph
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Problem 13) Two people drove their cars from the same place in opposite
directions. If they leave at the same time and one person A drives times as
fast as person B, and in hours, they are miles apart, what are their driving
speeds?
Solution:
From the problem, variable represents the first person and variable
represents the second person. We can write and solve the following equations:
Since , substitute for in the second equation and solve for :
Use to solve for
Answer: Person A drove mph; Person B drove mph
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Problem 14) Suppose you ride a bicycle to a store at a speed of miles/hour.
You then walk home at a speed of miles/hour. The total round trip time is
hours. How far from your starting point is the store?
Solution:
Let represent time in hours, represent the speed and represent the distance.
We know that the following formulas apply:
Substitute the values from the problem into the second formula:
Multiply the equation by :
Answer: miles
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Problem 15) Suppose you leave your house by bicycle and travel miles per
hour. One hour later, your brother leaves and travels down the same road by car
at miles per hour. How long, in hours to the nearest tenth, does it take for the
car to overtake the bicycle?
Solution:
When the car overtakes the bicycle, the distances each travel are the same. Thus
we can use the formula, where is the distance, is the time, is the bicycle and
is the car:
.
Substitute the numbers from the problem into the formula:
Answer: hours
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Problem 16) Two planes leave an airport and fly in opposite directions. One
plane flies at miles/hour and the other plane flies at miles per hour. How
many hours will it take for the two planes to be miles apart?
Solution:
Let represent the number of hours. Write and solve the following equation:
Answer: hours
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Problem 17) Two people leave from two towns that are miles apart and
travel toward each other along the same road. Person A drives miles/hour
(mph) slower than person B. If they meet in hours, at what speed did each
person travel?
Solution:
Using the variable as the speed of Person B and
as the speed of Person
A, we can write and solve following equation:
Person B’s speed:
Person A’s speed:
Answer: Person A’s speed: mph; Person B’s speed: mph
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Problem 18) Two people ride their bikes from the same place in opposite
directions. If they leave at the same time and person A rides times as fast as
person B, and in hours, they are miles apart, what are their riding speeds?
Solution:
From the problem, variable represents the first person and variable
represents the second person. We can write and solve the following equations:
Since , substitute for in the second equation and solve for :
Use to solve for
Answer: Person A rode mph; Person B rode mph
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Problem 19) Suppose you ride a bicycle to a store at a speed of miles/hour.
You then walk home at a speed of miles/hour. The total round trip time is
hours. How far from your starting point, in miles to the nearest two decimals, is
the store?
Solution:
Let represent time in hours, represent the speed and represent the distance.
We know that the following formulas apply:
Substitute the values from the problem into the second formula:
Multiply the equation by :
Answer: miles
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Problem 20) Suppose you leave your house by bicycle and travel miles per
hour. One hour later, your brother leaves and travels down the same road by car
at miles per hour. How long, in hours to the nearest tenth, does it take for the
car to overtake the bicycle?
Solution:
When the car overtakes the bicycle, the distances each travel are the same. Thus
we can use the formula, where is the distance, is the time, is the bicycle and
is the car:
.
Substitute the numbers from the problem into the formula:
Answer: hours
