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14 November, 18:34

A motorboat takes 3 hours to travel 144 km going upstream. The trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Rate of the boat still in water:

Rate of the current:

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  1. 14 November, 18:39
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    Let x be rate of boat in still water

    let y be rate of current

    we use this equation to relate quantities:

    distance = speed · time

    we have two unknowns so we might need to create a system of equationss

    upstream:

    speed (in km/h) = x - y

    (we get speed of boat then subtract the current's speed from it since current is going against boat direction)

    time = 3 hours

    distance = 144 km

    downstream:

    speed (in hm/h) = x + y

    (we get speed of boat then add the current's spd from it since current is going against boat direction)

    time = 2 hours

    distance = 144 km (same distance upstream and downstream)

    using distance = speed times time

    for upstream

    144 = 3 (x-y)

    144 = 3x - 3y

    for downstream

    144 = 2 (x+y)

    72 = x + y

    system of eqns:

    144 = 3x - 3y

    72 = x + y

    solve by substitution: move 72 = x + y into x = 72 - y and subst into other equation for x

    144 = 3 (72 - y) - 3y

    144 = 216 - 3y - 3y

    144 = 216 - 6y

    144 - 216 = - 6y

    -72 = - 6y

    y = 12 km/h

    Use x = 72 - y to find x with y = 12: x = 72 - 12 = 60 km/h

    rate of boat in still water is 60 km/h

    rate of the current is 12 km/h
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