Question 356938: Rachael runs 2 kilometers to a bus stop, and then rides 4.5 km to school. On average the bus is 45 km/hr faster than Rachael's average running speed. If the entire trip takes 25 minutes, how fast does Rachael run?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Rachael runs 2 kilometers to a bus stop, and then rides 4.5 km to school. On average the bus is 45 km/hr faster than Rachael's average running speed. If the entire trip takes 25 minutes, how fast does Rachael run?
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Running DATA:
distance: 2 km ; rate = x km/h ; time = 2/x hrs
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Bus DATA:
distance: 4.5 km ; rate = x+45 km/h ; time = 4.5/(x+45) hrs.
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Equation:
time + time = 25/60 hr
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2/x + 4.5/(x+45) = 5/12
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Multiply thru by 12x(x+45) to get:
24(x+45) + 12*4.5x = 5x(x+45)
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24x + 1080 + 54x = 5x^2 + 225x
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78x + 1080 = 5x^2 + 225x
5x^2 + 147x - 1080 = 0
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Positive solution:
x = 6.0868 km/h (running rate)
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Cheers,
Stan H.
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