# SOLVING PROPORTIONS WORD PROBLEMS WORKSHEET

Worksheet given in this section will be much useful for the students who would like to practice solving word problems proportions.

## Solving Proportions Word Problems Worksheet

Problem 1 :

Look at the picture below.

Janet drives from Clarkson to Humbolt in 2 hours. Suppose If she maintains the same driving rate, how many miles can she drive in 10 hours ?

Problem 2 :

The distance Ali runs in 40 minutes is 3 miles. At this rate, how far can he run in 60 minutes ?

Problem 3 :

In 15 minutes, Lena can finish 2 math problems. At that rate, how many math problems can she finish in 75 minutes ? Use a double number line to find the answer.

Problem 4 :

Ms. Reynolds has a system of 10 sprinklers that water her entire lawn. The sprinklers run one at a time, and each runs for the same amount of time. The first 4 sprinklers run for a total of 50 minutes. How long does it take to water her entire lawn ?

## Solving Proportions Word Problems Worksheet - Solutions

Problem 1 :

Look at the picture below.

Janet drives from Clarkson to Humbolt in 2 hours. Suppose If she maintains the same driving rate, how many miles can she drive in 10 hours ?

Solution :

Given : Janet drives from Clarkson to Humbolt in 2 hours.

From the above information, we can get the following ratio between time and distance.

2 : 112 -----> (1)

Let "A" be the number of miles that she can drive in 10 hours.

Then, we have

10 : A -----> (2)

Since she maintains the same driving rate, the ratios (1) and (2) are equivalent.

So, we get the proportion

2 : 112  =  10 : A

Let us apply cross product rule

2A  =  112 x 10

A  =  (112 x 10) / 2

A  =  560

So, she can drive 560 miles in 10 hours.

Problem 2 :

The distance Ali runs in 40 minutes is 3 miles. At this rate, how far can he run in 60 minutes ?

Solution :

Let "A" be the number of miles that he can run in 60 minutes.

From the given information, we can write the following proportion.

In the proportion

40 : 3  =  60 : A

the extremes are 40 & A and means are 3 & 60.

Let us apply cross product rule.

40A  =  3 x 60

Dividing by 40 on both sides, we get

A  =  180 / 40

A  =  9/2 or  4 1/2

At this rate, Ali can run 9/2 miles, or 4 1/2 miles, in 60 minutes.

Problem 3 :

In 15 minutes, Lena can finish 2 math problems. At that rate, how many math problems can she finish in 75 minutes ? Use a double number line to find the answer.

Solution :

Given : Lena can finish 2 math problems in 15 minutes.

From the above information, we can get the following ratio between math problems and minutes.

2 : 15 -----> (1)

Let "B" be the number of math problems that she can finish in 75 minutes.

Then, we have

B : 75 -----> (2)

Since she maintains the same rate, the ratios (1) and (2) are equivalent.

So, we get the proportion

2 : 15  =  B : 75

Let us apply cross product rule

2 x 75  =  15B

(2 x 75) / 15  =  B

10  =  B

So, Lena can finish 10 math problems in 75 minutes.

Problem 4 :

Ms. Reynolds has a system of 10 sprinklers that water her entire lawn. The sprinklers run one at a time, and each runs for the same amount of time. The first 4 sprinklers run for a total of 50 minutes. How long does it take to water her entire lawn ?

Solution :

Let "T" be the time takes to water the entire lawn.

From the given information, we can write the following proportion.

In the proportion

50 : 4  =  T : 10

the extremes are 50 & 10 and means are 4 & T.

Let us apply cross product rule.

50 x 10  =  4T

Dividing by 4 on both sides, we get

500 / 4  =  T

125  =  T

So, it takes 125 minutes or 2 hours 5 minutes to water her entire lawn.

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