<PRE><B>Question 309461</B>
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 = {{{1050/37.5}}}
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 = {{{880/4}}}
x = 220 mph speed of the plane
:
:
Check solution in 2nd equation where plane speed = 110 and boat speed = 35:
4(110) + 25(35) = 
440 + 875 = 1315</PRE>