Question 410235: If John runs a mile in 7 minutes and bikes a mile in 4 minutes, he will finish a run/bike race in 90 minutes. If he runs a mile in 8 minutes and bikes a mile in 3 minutes, he will finish the same race in just 84 minutes. How many miles will John have to run during this race?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If John runs a mile in 7 minutes and bikes a mile in 4 minutes, he will finish a run/bike race in 90 minutes.
7r + 4b = 90
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If he runs a mile in 8 minutes and bikes a mile in 3 minutes, he will finish the same race in just 84 minutes.
8r + 3b = 84
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How many miles will John have to run during this race?
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Solve the System:
Multiply thru 1st by 3 and 2nd by 4 to get:
21r + 12b = 3*90
32r + 12b = 4*84
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Subtract and solve for "r":
11r = 66
r = 6 (# of miles running)
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Solve for "b":
8r + 3b = 84
8*6 + 3b = 84
48 + 3b = 84
3b = 36
b = 12 (# of miles biking)
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Cheers,
Stan H.
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