Math CentralQuandaries & Queries


Subject: uniform motion
Name: bob
Who are you: Other

A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current?


Use the fact that distance is velocity multiplied by time: d = v x t.

The boat's velocity is going to be its velocity relative to the water, plus the velocity of the current.

d = (vboat + vcurrent) x t

Let v be the velocity of the current downstream (you could pick upstream here, but I felt like picking downstream). Then the velocity of the current upstream (if we keep the boat's velocity at positive 16 miles per hour) is -v. The distance travelled going upstream is the same as the distance downstream.

From here can you set up an equation that lets you solve for v?


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