SOLUTION: Two ships travelling from Dumaguete to Cagayan de Oro differ in average speed by 10 kph. The slower ship takes 3 hours longer to travel a 240 kilometer route than for the faster sh

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Question 1045713: Two ships travelling from Dumaguete to Cagayan de Oro differ in average speed by 10 kph. The slower ship takes 3 hours longer to travel a 240 kilometer route than for the faster ship to travel a 200 kilometer route. Find the speed of the slower ship. Hint: Construct an equation with time t as the variable.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
From the hint that you gave, it should follow that
200%2Ft+-+240%2F%28t%2B3%29+=+10.
===> 20%2Ft+-+24%2F%28t%2B3%29+=+1.
<===> -4t%2B60+=+t%5E2%2B3t, after simplifying;
<===> t%5E2+%2B+7t+-60+=%28t%2B12%29%28t-5%29+=+0
==> t = 5 hours
===> The speed of the slower ship is 240%2F%28t%2B3%29+=+240%2F%285%2B3%29+=+240%2F8+=+30+kph.

ALTERNATE SOLUTION (without initially resorting to t):
Let r = speed of the slower ship.
===> r + 10 = speed of the faster ship
===> 240%2Fr+-+200%2F%28r%2B10%29+=+3
===> r = 30 kph, which gives the speed of the slower ship directly.