Math CentralQuandaries & Queries


Question from Jan, a student:

A 3 hour river cruise goes 15km upstream and then back again.The river has a current speed of 2km/h.what is the boat's speed and how long was the upstream journey?

Hi Jan,

The crucial fact here is that speed is distance divided by time.

Suppose that the boat speed in still water is $s$ km/hr and the trip upstream takes $t$ hours. On the upstream par of the trip the boat is travelling against the current so its speed s $v - 2$ km/hr. Use the fact that speed is distance divided by time to write ann equation in $v$ and $t$ for this part of the trip.

What is the speed of the boat on the downstream part of the trip? what is the time required for this part of the trip? Write an equation in $v$ and $t$ for the downstream part of the trip.

Solve the resulting equations for $v$ and $t.$ Verify your answer by using these values to show that the time required is 3 hours.

I hope this helps,

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