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

**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 ?

**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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