How far did he go?

Question

A man rides out into the country at a uniform rate of 30 miles per hour. He rests 2 hours and
then rides back at 20 miles per hour. He is gone 5 hours. How far did he go?

Answer 1

Hi Dharsan, we need to set up a system of equations.

 

If he is gone for 5 hours, 2 of which he rested, he rode for 3 hours. Let X represent the time riding into the county, and let Y represent the time riding out of the country.

 

1) The first equation is    x + y = 3

 

The distance into and out of the country is same, and since distance = speed times time

 

2) The second equation is 30x = 20y

 

We can solve this system by substitution

1) x = 3 - y

2) 30(3 - y) = 20y

3) 90 - 30y = 20y

4) 90 = 50y

5) y = 1.8

 

So he rode 1.8 hours at a speed of 20 miles / hour, which means he rode 36 miles one way

 

Since distance is the same into the country and back out of the country, he rode a total of 72 miles 

 

 

*note* we solved for y and multiplied by 20 to get distance one way...we could have also solved for x and multiplied by 30 and arrived at the same answer because distance is equal there and back