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 the actual speed and the speed of the ship had been one-fourth gre
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Question 400002: 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 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 lenght of time. What are the speeds of the plane and the ship
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
