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 0ne-f
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Question 426858: 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 0ne-fourth greater, the person would have traveled only 1315 miles in the same length of time. What is the speed 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-forth 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 plane
and
Let y = speed of ship
:
Two distance equations; dist = time * speed
:
4x + 25y = 1580
and
4(.5x) + 25(1.25y) = 1315, (plane half speed, boat 1.25 original speed)
2x + 31.25y = 1315
:
Multiply above equation by 2. Subtract the first equation
4x + 62.5y = 2630
4x + 25y = 1580
---------------------subtraction eliminates x, find y:
37.5y = 1050
y =
y = 28 mph speed of the ship
:
Find x using the 1st equation
4x + 25(28) = 1580
4x + 700 = 1580
4x = 1580 - 700
4x = 880
x =
x = 220 mph speed of the plane
:
:
Check solution in 2nd equation, plane half speed, boat 1.25 original speed:
4(110) + 25(35) =
440 + 875 = 1315
