Question 126254
A person traveling 4 hour by plane and 25 hour by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and 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.
:
Originally
Let x = speed of the plane (mph)
Let y = speed of the ship
If:
.5x = speed of the plane
1.25y = speed of the ship
:
Write two distance equations: Distance = time * speed
:
Actual event equation:
4x + 25y = 1580
:
If event equation:
4(.5x) + 25(1.25y)
2x + 31.25y = 1315 
:
Use elimination here. Multiple above equation by 2, subtract "Actual" equation:
4x + 62.5y = 2630
4x + 25y = 1580
-------------------Subtracting eliminates x
0x + 37.5y = 1050
y = {{{1050/37.5}}}
y = 28 mph is the ships original speed
:
Use equation; 4x + 25y = 1580; substitute 28 for y:
4x + 25(28) = 1580
4x = 700 = 1580
4x = 1580 - 700
4x = 880
x = {{{880/4}}}
x = 220 mph plane's original speed
:
:
Check our solutions in the "If event" equation
4(.5(220)) + 25(1.25(28)) = 
440 + 875 = 1315