SOLUTION: Suppose that a cyclist began a 442 mile ride across the western edge of the state, at the same time that a car traveling toward it leaves the eastern edge of the state. If the bike

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Question 998213: Suppose that a cyclist began a 442 mile ride across the western edge of the state, at the same time that a car traveling toward it leaves the eastern edge of the state. If the bike and the car met after 8.5 hours and the car traveled 30.8 MPH faster than the bike, find the average rate of each
Found 2 solutions by mananth, josgarithmetic:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Let cyclist speed be x mph
car speed = (x+38.5) mph
both of them take the same time to meet = 8.5 hours
Distance = 442 miles
Combined speed = 2x+38.5
t= d/r
8.5 = 442/(2x+38.5)
8.5(2x+38.5) =442
17x + 327.5 = 442
17x= 442-327.5
17x = 114.5
x=6.75 mph...cycle speed
add 38.5 to get car speed

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
              speed          time         distance
CYCLIST        r             8.5         %28r%29%288.5%29
CAR           r+30.8         8.5         %28r%2B30.8%29%288.5%29
Total                                    442


Total distances of both is the distance between the two borders of the state.
%28r%29%288.5%29%2B%28r%2B30.8%29%288.5%29=442, and solve for r.

The question to obtain the answer is %28r%2B%28r%2B30.8%29%29%2F2, for AVERAGE RATE OF EACH.