# 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.

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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