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Math Help - How can I solve this (Word problem grade 11)?

  1. #1
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    How 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
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  2. #2
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    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
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