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

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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) About Me  (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) 4Rp+%2B+25Rs+=+1580
We are now given additional information and it looks like this:
(ii) %281%2F2%29Rp%2A4+%2B+%285%2F4%29Rs%2A25+=+1315
multiply (ii) by 2 and we get
(iii) 4Rp+%2B+62.5Rs+=+2630
Solve (i) for 4Rp and we get
(iv) 4Rp+=+1580+-+25Rs
substituting (iv) into (iii), we get
(v) 1580+-+25Rs+%2B+62.5Rs+=+2630
solving for Rs, we get
(vi) 1580+%2B37.5Rs+=+2630
and then
(vii) 37.5Rs+=+1050
So,
Rs = 28
and
Rp = 220.