Math CentralQuandaries & Queries


Question from Simon, a student:

Two boats, one travelling towards the east and the other travelling towards the north, are 10 km apart afetr an hour. If the speed of one boat is 2 more than the speed of the other boat, what is the speed of the faster boat?

Hi Simon. I assume the boats started next to each other before the hour of travel.

Let x = the speed of the faster boat. Then x-2 is the speed of the slower boat.

They traveled for the same length of time (1 hour). Since speed times time equals distance, that means the fast boat went x(1) = x km and the slow boat went (x-2)(1) = x-2 km.

The two directions are perpendicular, which means that you can draw a right triangle with the right angle representing the starting point and the hypotenuse representing the distance between the boats after one hour.

Thus you have a right triangle whose legs are x and x-2 km and whose hypotenuse is 10 km.

What does Pythagoras tell you about the relationship of these quantities? Can you use that to create a quadratic equation? Does it factor?

Hope this helps,
Stephen La Rocque

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