A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:45610
Question
A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:45610
Solution
Let's denote the speed of the stream as 'x' km/hr.
When the boat is going downstream (with the current), its effective speed is (15 + x) km/hr.
When the boat is going upstream (against the current), its effective speed is (15 - x) km/hr.
The total time taken for the boat to travel 30 km downstream and then 30 km upstream is given as 4 hours and 30 minutes, which is 4.5 hours.
We can set up the following equation using the formula time = distance/speed:
30/(15 + x) + 30/(15 - x) = 4.5
Solving this equation will give us the speed of the stream.
First, let's multiply through by (15 + x)(15 - x) to get rid of the fractions:
30(15 - x) + 30(15 + x) = 4.5(15² - x²)
450 - 30x + 450 + 30x = 4.5(225 - x²)
900 = 1012.5 - 4.5x²
Subtract 900 from both sides:
4.5x² = 112.5
Divide by 4.5:
x² = 25
Take the square root of both sides:
x = 5
So, the speed of the stream is 5 km/hr.
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