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-forth

Algebra ->  Customizable Word Problem Solvers  -> Travel -> 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-forth       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 166998: 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.
Answer by ankor@dixie-net.com(22740) About Me  (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 shipe
:
Two distance equations; dist = time * speed
:
4x + 25y = 1580
and
4(.5x) + 25(1.25y) = 1315
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 = 1050%2F37.5
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 = 880%2F4
x = 220 mph speed of the plane
:
:
Check solution in 2nd equation:
4(110) + 25(35) =
440 + 875 = 1315