Question 107934: A person traveling 4 hr by plane and 25 hr 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 speeds of the plane and the ship.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A person traveling 4 hr by plane and 25 hr 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 speeds of the plane and the ship.
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Let x = speed of the plane
Let y = speed of the ship
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Write two distance equations; Distance = time * speed
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"Actual" equation:
4x + 25y = 1580
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The "If" equation:
.5(4x) + 1.25(25y) = 1315
or
2x + 31.25y = 1315
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Multiply the above equation by 2, subtract the "actual" equation
4x + 62.5y = 2630
4x + 25.0y = 1580
------------------- subtracting eliminates x
0x + 37.5y = 1050
y = 1050/37.5
y = 28 mph is the actual speed of the ship
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Find x using the "actual" equation
4x + 25(28) = 1580
4x + 700 = 1580
4x = 1580 - 700
x = 880/4
x = 220 mph is the actual speed of the plane
:
:
Check solution using the "IF" equation
.5(4*220) + 1.25(25*28) =
440 + 875 = 1315
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