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Boats & Streams, Pipes & Cisterns · Question 35 of 85

Question 35

HardOriginal question

A boat moves at 15 km/h in still water. It goes 30 km downstream and comes back in 4 hours 30 minutes in all. What is the speed of the stream?

Options for question 35

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. 3015+s+3015−s=4.5\frac{30}{15 + s} + \frac{30}{15 - s} = 4.5, which gives 900225−s2=4.5\frac{900}{225 - s^{2}} = 4.5.

  2. 225−s2=200225 - s^{2} = 200, so s2=25s^{2} = 25 and s=5s = 5 km/h.

Worth noting

Check 3 km/h: 3018+3012=123+212\frac{30}{18} + \frac{30}{12} = 1\frac{2}{3} + 2\frac{1}{2} hours, short of 4.5.

Concept
The stream's speed from a round trip
Typical time
120 s
Your time
—
The rule this testsJourneys on a river
Practise this chapter →

Ten questions from Boats & Streams, Pipes & Cisterns, at your own pace.

Practise this chapter →

Ten questions from Boats & Streams, Pipes & Cisterns, at your own pace.