Question

Two towns are 1,100 miles apart. A group of hikers Starts from each town and walks down the trail toward each other. They meet after a total hiking time of 240 hours. If one group travels 2 1/2 mile per hour slower than the other group, find the rate of each group.

Answer 1

3.54 and 1.04

Explanation:

Given:

Two towns are 1,100 miles apart.

A group of hikers Starts from each town and walks down the trail toward each other..

They meet after a total hiking time of 240 hours.

If one group travels 2 1/2 mile per hour slower than the other group.

Question asked:

Find the rate of each group.

Solution:

Let speed of faster hiker =
`x\ mph`

Speed of slower hiker =
`x-(5)/(2)\ mph`

As we know:

`Distance=speed* time`

Total distance between two town = Total combined speed of both hikers
`*`Total combined time taken

`1100=(x+x-(5)/(2) )*240\\ \\ Dividing\ both\ sides\ by\ 240\\ \\ 4.58=(x+x-(5)/(2) )\\ \\ 4.58=2x-(5)/(2) \\ \\Adding\ both\ sides\ by\ (5)/(2) \\ \\ 4.58+ (5)/(2)=2x- (5)/(2)+ (5)/(2)\\ \\ (2*4.58+5)/(2) =2x\\ \\ (14.16)/(2) =2x\\ \\ By \ cross\ multiplication\\ \\ 2*2x=14.16\\ \\ 4x=14.16`

`By\ dividing\ both\ sides\ by \ 4\\ \\ x=3.54\ miles\ per\ hour`

Speed of faster hiker =
`x\ mph` = 3.54 miles per hour.

Speed of slower hiker =
`x-(5)/(2)\ mph` =

`3.54-(5)/(2) =3.54-2.5=1.04\ miles\ per\ hour`

Therefore, speed of faster hiker is 3.54 miles per hour and speed of slower hiker is 1.04 miles per hour.