Math CentralQuandaries & Queries


Question from Adam, a parent:

The current in a stream moves at a speed of 2 km/h. A boat travels 38 km upstream and 38 km downstream in a total time of 3 hr. What is the speed of the boat in still water?

Hi Adam,

The key here is that rate is distance divided by time. The units tell you that, your rate is in kilometers divided by hours.

Suppose that the speed of the boat in still water is $s$ kilometers per hour and it takes $t$ hours to travel the 38 km upstream. When the boat is travelling upstream, against the current, its speed is $s - 2$ kilometers per hour. Hence, since rate is distance divided by time,

\[s-2 = \frac{38}{t}.\]

What is the speed of the boat when travelling downstream? How long does it take for the boat to travel the 38 kilometers downstream? Write a similar equation to the one above. Solve the two equations for $t$ and $s.$


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