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7 September, 18:02

It takes a boat going upstream 5 hours to cover the same distance, as it would cover in 3 hours going downstream. What is the speed of the boat if the speed of the current is 2 kilometers per hour?

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  1. 7 September, 18:18
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    The speed of the boat is 8 km/h.

    Step-by-step explanation:

    Assuming that the boat's speed is "x" without the influence of the current, then when it's going upstream it's speed is "x - 2" and when it's going downstream it's speed is "x + 2". Assuming that the distance is "y", we can then apply the formula for average speed in both cases to create a system of equations as shown below:

    speed = distance / time

    Upstream:

    x - 2 = y / 5

    5*x - 10 = y

    5*x - y = 10

    Downstream:

    x+2 = y / 3

    3*x + 6 = y

    3*x - y = - 6

    System:

    5*x - y = 10

    3*x - y = - 6

    Multiplying the second equation by - 1:

    5*x - y = 10

    -3*x + y = 6

    Adding both equations:

    2*x = 16

    x = 16/2 = 8 km/h

    The speed of the boat is 8 km/h.
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