**Solving proportions word problems worksheet :**

Worksheet on solving word problems is much useful to the students who would like to practice problems on solving real world problems with proportions.

1. Look at the picture given 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 ?

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

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.

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 ?

**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

Hence, 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

Hence, 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

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

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