A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an ho

Discussion in 'Calculator Requests' started by math_celebrity, May 13, 2020.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey?

    Set up the relationship of still water speed and downstream speed
    Speed down stream = Speed in still water + speed of the current
    Speed down stream = x+2

    Therefore:
    Speed upstream =x - 2

    Since distance = rate * time, we rearrange to get time = Distance/rate:
    15/(x+ 2) + 15 /(x- 2) = 3

    Multiply each side by 1/3 and we get:
    5/(x + 2) + 5/(x - 2) = 1

    Using a common denominator of (x + 2)(x - 2), we get:
    5(x - 2)/(x + 2)(x - 2) + 5(x + 2)/(x + 2)(x - 2)
    (5x - 10 + 5x + 10)/5(x - 2)/(x + 2)(x - 2)
    10x = (x+2)(x-2)

    We multiply through on the right side to get:
    10x = x^2 - 4

    Subtract 10x from each side:
    x^2 - 10x - 4 = 0

    This is a quadratic equation. To solve it, we type it in our search engine and we get:
    Speed of the boat in still water =X=5 +- sq. Root of 29 kmph

    We only want the positive solution:
    x = 5 + sqrt(29)
    x = 10.38

    Calculate time for upstream journey:
    Time for upstream journey = 15/(10.38 - 2)
    Time for upstream journey = 15/(8.38)
    Time for upstream journey = 1.79

    Calculate time for downstream journey:
    Time for downstream journey = 15/(10.38 + 2)
    Time for downstream journey = 15/(12.38)
    Time for downstream journey = 1.21
     

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