It took a crew 80 min to row 3 km upstream and back again. If the rate of flow of the stream was 3 km/h, what was the rowing rate of the crew?

The answer is : 6 km/h

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- Nov 3rd 2010, 05:45 PMSorenaHow can I solve this (Word problem grade 11)?
It took a crew 80 min to row 3 km upstream and back again. If the rate of flow of the stream was 3 km/h, what was the rowing rate of the crew?

The answer is : 6 km/h - Nov 3rd 2010, 06:09 PMGusbob
Split the trip into two parts. Once upstream, one downstream.

Let rowing rate be v.

__Upstream__

Total speed of the boat is (v - 3) km/h because for every hour, the crew rows vkm/h x 1h = v km. But in that same hour, the stream drags them back 3km/h x 1h = 3km. Total distance travelled in this hour is thus v-3, giving the velocity of (v-3)km/h.

__Downstream__

This time, the crew rows v km in one hour and the stream carries them an extra 3km in that hour. So velocity going downstream is (v+3) km/h

Now the total distance travelled is 3km upstream and 3km downstream

Since time = distance/speed, we can write

T1 = time spend rowing upstream = 3/(v-3) hours

T2 =time spend rowing downstream =3/(v+3) hours

This was accomplished in 80 minutes total, which is 1.333... hours

So Ttotal = T1 + T2 = 3/(v-3) + 3/(v+3) = 1.333...

The solution to this is v = 6km/h