SOLUTION: 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-

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Question 120766: 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 speeds of the plane and the ship.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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 speeds of the plane and the ship.
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Let x = original speed of the plane
Let y = original speed of the ship
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Then:
.5x = the "if" speed of the plane
1.25y = the "if" speed of the ship
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An equation for the statement:
"A person traveling 4 hours by plane and 25 hours by ship covers 1580 miles."
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4x + 25y = 1580; call it the original equation
:
:
An equation for the statement:
"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."
4(.5x) + 25(1.25y) = 1315
2x + 31.25y = 1315; call it the "If" equation
:
Multiply the above equation by 2 and subtract the original equation
4x + 62.5y = 2630
4x + 25y = 1580
-------------------subtracting eliminates x, find y:
0x + 37.5y = 1050
y = 1050%2F37.5
y = 28 mph is the original speed of the ship
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Use the original equation to find the speed of the plane
4x + 25(28) = 1580
4x = 1580 - 700
4x = 880
x = 220 mph is the original speed of the plane
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You can check the solution in the "if" equation
2(220) + 31.25(28) =