SOLUTION: A person traveling 4hr 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-fourth g

Question 258041: A person traveling 4hr 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-fourth greater, the person would have traveled only 1315 miles in the same length of time. Find the speeds of the plane and ship?
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
This is an RTD problem. Let RS = rate of ship, and Rp = rate of plane. Here is a table based on the given information:
transport . . . . . . . .rate . . . . . . . .time . . . . . . .distance
PLANE . . . . . . . . . .Rp . . . . . . . . .4 . . . . . . . . .4Rp
SHIP . . . . . . . . . .Rs . . . . . . . . . .25 . . . . . . . . 25Rs
TOTAL . . . . . . . . . . . . . . . . . . . .29 . . . . . . . . .1580
So, we get from column 3,
(i)
We are now given additional information and it looks like this:
(ii)
multiply (ii) by 2 and we get
(iii)
Solve (i) for 4Rp and we get
(iv)
substituting (iv) into (iii), we get
(v)
solving for Rs, we get
(vi)
and then
(vii)
So,
Rs = 28
and
Rp = 220.

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