SOLUTION: a bicyclist and a hiker leave the same place at the same time and travel in the same direction.the bicyclist travels 3 times as fast as the hiker.at the end of 3 hours they are 24

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Question 153445: a bicyclist and a hiker leave the same place at the same time and travel in the same direction.the bicyclist travels 3 times as fast as the hiker.at the end of 3 hours they are 24 miles apart.how fast does the hiker travel?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Remember:
speed=x%28mi%2Fhr%29 of the bicyclist and hiker:
hiker=h=x%28mi%2Fhr%29
biker=b=3x%28mi%2Fhr%29, 3 times faster
Equating the 2 speeds and adding the speed (separation) of 24 miles in 3 hours to the hiker since the bicyclist is faster than the hiker:
hiker=biker
%28x%28mi%2Fhr%29%29+%2B%2824mi%2F3hr%29=3x%28mi%2Fhr%29
%28cross%2824%298mi%2Fcross%283%29hr%29=3x%28mi%2Fhr%29-x%28mi%2Fhr%29
8%28mi%2Fhr%29=2x%28mi%2Fhr%29 ----> cross%288%294%28mi%2Fhr%29=cross%282%29x%28mi%2Fhr%29
x=4%28mi%2Fhr%29 ---------------------> speed of the hiker
For bicyclist:
3%2A4=12%28mi%2Fhr%29 ------------------> speed of the bicyclist
to check, lets calculate the distance in 3 hours:
hiker: 4%28mi%2Fcross%28hour%29%29%283cross%28hours%29%29=12miles
biker: 12%28mi%2Fcross%28hour%29%29%283cross%28hours%29%29=36miles
IT'S TRUE THAT AFTER 3 HOURS, THE DISTANCE SEPARATING THEM IS 36-12=24miles
Thank you,
Jojo