Respuesta :
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 = [tex]x\ mph[/tex]
Speed of slower hiker = [tex]x-\frac{5}{2}\ mph[/tex]
As we know:
[tex]Distance=speed\times time[/tex]
Total distance between two town = Total combined speed of both hikers [tex]\times[/tex]Total combined time taken
[tex]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[/tex]
[tex]By\ dividing\ both\ sides\ by \ 4\\ \\ x=3.54\ miles\ per\ hour[/tex]
Speed of faster hiker = [tex]x\ mph[/tex] = 3.54 miles per hour.
Speed of slower hiker = [tex]x-\frac{5}{2}\ mph[/tex] =
[tex]3.54-\frac{5}{2} =3.54-2.5=1.04\ miles\ per\ hour[/tex]
Therefore, speed of faster hiker is 3.54 miles per hour and speed of slower hiker is 1.04 miles per hour.
