SOLUTION: Word problems using inequalities. Please help Jeff bikes for three hours and his brother bikes four hours. Although Jeff bikes 15 mph faster, his total distance was at most t

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Question 166763This question is from textbook Algebra 1
: Word problems using inequalities. Please help
Jeff bikes for three hours and his brother bikes four hours. Although Jeff bikes 15 mph faster, his total distance was at most twice as far as his brother's. How fast does each ride?
Thank you,
Joe This question is from textbook Algebra 1

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

Working Eqn ----> Speed=Distance%2Ftime
Conditions:
Speed of Jeff: S%5Bjf%5D=x%2B15, 15mph faster than brother
Speed of brother: S%5Bbr%5D=x
Distance covered by Jeff in t%5Bjf%5D=3hours: D%5Bjf%5D=2%2AD%5Bbr%5D, twice that of brother covered in t%5Bbr%5D=4hours
Via Working eqn,
D=%28Speed%29%28time%29
We equate the 2 distances by both:
D%5Bjf%5D=2D%5Bbr%5D
%28S%5Bjf%5D%29%28t%5Bjf%5D%29=2%28%28S%5Bbr%5D%29%28t%5Bbr%5D%29%29
%28x%2B15%29%283hrs%29=2%28%28x%29%284hrs%29%29
3x%2B45=8x
45=8x-3x=5x ----> cross%2845%299%2Fcross%285%29=cross%285%29x%2Fcross%285%29
highlight%28x=9mph%29, Speed of brother
9%2B15=highlight%2824mph%29, Speed of Jeff
In doubt? Let's check their distance, via working eqn,
Distance covered by Jeff is twice as much ----> D%5Bjf%5D=%2824%29%283%29=72miles
D%5Bbr%5D=%289%29%284%29=36miles%29
Thank you,
Jojo