Question 161627
let x = rate of the plane.
let y = rate of the ship.
first equation is:
4*x + 25*y = 1580.
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since the plane traveled 4 hours at half rate of speed, and the ship traveled 25 hours at 1.25 rate of speed, the second equation becomes
2*x + 31.25*y = 1315.
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this is because 4 * x/2 = 2*x, and 25 * (5/4*y) = 125/4 * y = 31.25 * y.
the distance traveled under these new rates of speed is 1315.
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we have 2 equations with 2 unknowns.
4*x + 25*y = 1580
2*x + 31.25*y = 1315.
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multiply the bottom equation by 2 so we can eliminate the x.
equations become
4*x + 25*y = 1580
4*x + 62.5*y = 2630
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subtract top equation from bottom equation to get
37.5*y = 1050
y = 28
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if y = 28, we can solve for x in either equation.
use 4*x + 25*y = 1580
this becomes
4*x + 700 = 1580
4*x = 880
x = 220
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x = 220 = rate of plane
y = 28 = rate of ship
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to prove, take 1/2 the rate of the plane and 1.25 times the rate of the ship to solve the second equation.
1/2 * 220 = 110.
5/4 * 28 = 35
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4*110 + 25*35 = 1315 which proves the values of x and y are good in both equations.
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answer is:
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plane travels at 220 miles per hour for 4 hours.
ship travels at 28 miles per hour for 25 hours.
total distance traveled is 1580 miles.
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plane travels at 110 miles per hour for 4 hours.
ship travels at 35 miles per hour for 25 hours.
total distance traveled is 1315 miles.
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110 is half of 220.
35 is 5/4 * 28.
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x = 220
y = 28