A person traveling 4 hr by plane and 25 hr by ship covers 15

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 0ne-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.
Thank you.

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let x=speed of plane
And let y=speed of the ship
Distance initially travelled by plane=4x
Distance initially travelled by ship=25y so:
4x+25y=1580----------------------------------eq1
and
4(x/2)+25(5y/4))=1315 (Note: 1/4 greater than y=4y/4+y/4=5y/4)- multiply each term by 4
8x+125y=5260----------------------------------eq2
multiply eq1 by 2, and we get:
8x+50y=3160
and then subtract it from eq2:
75y=2100 divide both sides by 75
y=28 mph---------------speed of ship
substitute y=28 into eq1
4x+25*28=1580
4x+700=1580 subtract 700 from each side
4x=880 divide each side by 4
x=220 mph speed of plane
CK
220*4+25*28=1580
880+700=1580
1580=1580
and
(1/2)*220*4+25*(5/4)*28=1315
440+875=1315
1315=1315