math

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CTHook CTHook
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math

Bernard raced twice as fast as the local bike racer. For this reason he raced 120 miles in 3 hours less than it took the bike racer to race 105 miles.  How fast did each travel?  What was the time of each racer?
McGenius McGenius
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Re: math

distance = rate x time
d = rt

rate = distance/time

t = local racer's time
t - 3 = Bernard's time

120           105
----- = 2( -------)  Bernard's rate is twice as fast as local racer's rate
t - 3            t

120      210
----- = ------   multiplied by 2
t - 3        t

120t = 210t - 630   cross-multiplied
-90t = -630   subtracted 210t
t = 7   divided by -90
t - 3 = 4   substituted

local racer's time is 7
Bernard's time is 4

120/(t - 3) = Bernard's rate
= 120/4
= 30 is Bernard's rate

105/t = local racer's rate
= 105/7
= 15 is local racer's rate

*McGenius*