Question 178780
A bicycle rider travels 18 miles in the same amount of time that it takes a jogger to travel 10 miles. If the bicyclist goes 9.6 miles per hour faster than the jogger, how fast does each person travel?
:
distance = rate * time
:
let r be the rate of the jogger...therefore rate of the bike rider is r+9.6
times are equal
:
bike:18=(r+9.6)t...eq 1
jogger:10=rt.......eq 2
:
rewrite eq 2 to t=10/r and plug that into eq 1
:
18=(r+9.6)(10/r)
:
18r=10(r+9.6)......multiplied both sides by r
:
18r=10r+96
:
8r=96
:
{{{highlight(r=12)}}}mph-speed of jogger
:
{{{highlight(r+9.6=12+9.6=21.6)}}}mph-speed of bike rider