SOLUTION: 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
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Question 145797: 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!
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.
:
Let x = speed of the plane
and
Let y = speed of the boat
:
"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."
Then
.5x = speed of the plane
and
1.25y = speed of the boat
:
When they say," the person would have traveled only 1315 miles in the same length of time."
I assume they still mean 4 hrs in the plane and 25 hrs in the boat.
If they mean only that the total time is 29 hrs it's a different problem.
:
Two equations:
4x + 25y = 1580
and
.5(4x) + 1.25(25y) = 1315
2x + 31.25y = 1315
Multiply this equation by 2 and subtract the 1st equation from it
4x + 62.5y = 2630
4x + 25y = 1580
-------------------subtracting eliminates x
37.5y = 1050
y =
y = 28 mph is the speed of the boat
:
Find the speed of the plane using the 1st equation:
4x + 25(28) = 1580
4x + 700 = 1580
4x = 1580 - 700
x =
x = 220 mph is the speed of the plane
:
:
Check using the "if" situation:
4(110) + 25(35) = 1315
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