SOLUTION: A cabin cruiser leaves a harbour and travels south at 15km/h. One hour later a speed boat leaves the same harbour and travels on the same course at 25 km/h. How far from the harbou

Question 1173675: A cabin cruiser leaves a harbour and travels south at 15km/h. One hour later a speed boat leaves the same harbour and travels on the same course at 25 km/h. How far from the harbour will the speed boat pass the cruiser?
Found 3 solutions by Boreal, MathTherapy, greenestamps:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
One way is the cabin cruiser has a 15 km head start and is being caught at 10 km/h, so it is 1.5 hours chase and 2.5 hours after leaving the harbor, or 37.5 km.
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another way is cruiser has gone 15km/h*x h km.
the speed boat has gone 25 km/h (x-1) h km.
Set those equal to each other'
15x=25x-25
10x=25
x=2.5 hours, time the cabin cruiser has gone 15*2.5 or 37.5 km and the speed boat 25*1.5 or 37.5 km.
Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

A cabin cruiser leaves a harbour and travels south at 15km/h. One hour later a speed boat leaves the same harbour and travels on the same course at 25 km/h. How far from the harbour will the speed boat pass the cruiser?

Let distance from the harbour, be D
Then time the slower boat took to get to that point =
And, time the faster took to get to that point =
We then get the following TIME equation:
5D = 3D + 75 ------ Multiplying by LCD, 75
5D - 3D = 75
2D = 75
Distance from the harbour, or
Answer by greenestamps(13208)   (Show Source): You can put this solution on YOUR website!

The cabin cruiser travels 15km in the 1 hour before the speedboat starts.

The rate at which the speedboat overtakes the cabin cruiser is the difference between their speeds, which is 25-15=10 km/h.

The time required to make up 15km at a rate of 10 km/h is 15/10 = 1.5 hours.

In 1.5 hours the speedboat will travel 25*1.5 = 37.5km.

ANSWER: The speedboat will overtake the cabin cruiser 37.5 km from the harbor.

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