Question 153443: a person traveling 4 hours by plane and 25 hours by ship covers 1580 miles.if the speed of the plane had been one half of the actual speed and the speed of the ship had been one fourth greater,the person would have traveled only 1315 miles in the same length of time.find the speed of the plane and the ship.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a person traveling 4 hours by plane and 25 hours by ship covers 1580 miles.
if the speed of the plane had been one half of the actual speed
and the speed of the ship had been one fourth greater,
the person would have traveled only 1315 miles in the same length of time.
find the speed of the plane and the ship.
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Let p be the plane speed and s be the ship speed.
4p + 25s = 1580
4(p/2) + 25(5/4)s = 1315
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Rearrange:
4p + 25s = 1580
2p + (125/4)s = 1315
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Multiply thru 2nd equation by 2 to get:
4p + 25s = 1580
4p + (125/2)s = 2630
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Subtract the 1st equation from the 2nd to get:
(75/2)s = 1050
s = 28 mph (ship's speed)
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Substitute s = 28 into 4p + 25s = 1580 to solve for "p"
4p + 25*28 = 1580
4p + 700 = 1580
4p = 880
p = 220 mph (plane's speed)
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Cheers,
Stan H.
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