Distance and Rate Word Problems Math

Introduction to distance and rate word problem:

In mathematics education, the term word problem is often used to refer to any mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation. As word problems often involve a narrative of some sort, they are occasionally also referred to as story problems.

Here, we are going to see about word problems on distance and rate measurement in math. A few examples of word problems on distance and rate is given below which helps you for learning distance and rate word problems in math.

(Source: Wikipedia)

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Example of word problems on distance and rate:


Word problem 1:

Rohit left office and drove his car at the rate of 55 miles per hour for 3 hours. He stopped his car for few minutes and then he drove it for another 2 hours at the rate of 50 miles per hour to reach his home. Calculate how many miles did Rohit drive?

Solution:

The total distance travelled by Rohit is given by

Distance, D = (55 * 3) + ( 50 * 2)

= 165 + 100

= 265

So, total distance travelled by Rohit is 265 miles.

Word problem 2:

Nick travelled from place A to place B by bike in 4 hours. Chan travelled the same distance in 3 hours at a rate 30 miles per hour greater than Nick's. Calculate the distance between the two places.

Solution:

Let X be the rate at which Nick travelled between the two places.

Therefore, X + 30 be the rate at which Chan travelled between the two places.

So, the distance travelled by Nick is given by

Distance, D = Rate * Time = 4X ....................... (1)

Distance travelled by Chan is given by

Distance, D = Rate * Time = 3(X + 30) ............... (2)

From equation (1), we get

X = D/4

Substitute X = D/4 in equation (2).

D = 3(X + 30)

D = 3(D/4 + 30)

4D = 3(D + 120)

4D = 3D + 360

D = 360

Therefore, the distance between the two places is 360 miles.

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Homework problems:


1) Mick left from city A and drove his car at the rate of 70 miles per hour for 4 hours. He stopped his car for few minutes and then he drove it for another 4 hours at the rate of 60 miles per hour to reach city B. Calculate how many miles did Mick drive?

2) Morkel travelled from City A to City B by car in 3 hours. Joseph travelled the same distance in 2 hours at a rate 20 miles per hour greater than Morkel's. Calculate the distance between the two cities.

Solutions:

1) Total distance travelled by Mick is 520 miles.

2) Distance between the two cities 120 miles.