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

Answer:

3.54 and 1.04

Step-by-step 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 = $x-\frac{5}{2}\ mph$

As we know:

$Distance=speed\times time$

Total distance between two town = Total combined speed of both hikers $\times$Total combined time taken

$1100=(x+x-\frac{5}{2} )\times240\\ \\ Dividing\ both\ sides\ by\ 240\\ \\ 4.58=(x+x-\frac{5}{2} )\\ \\ 4.58=2x-\frac{5}{2} \\ \\Adding\ both\ sides\ by\ \frac{5}{2} \\ \\ 4.58+ \frac{5}{2}=2x- \frac{5}{2}+ \frac{5}{2}\\ \\ \frac{2\times4.58+5}{2} =2x\\ \\ \frac{14.16}{2} =2x\\ \\ By \ cross\ multiplication\\ \\ 2\times2x=14.16\\ \\ 4x=14.16$

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

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

Speed of slower hiker = $x-\frac{5}{2}\ mph$ =

$3.54-\frac{5}{2} =3.54-2.5=1.04\ miles\ per\ hour$

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