Question 60

A boat goes a distance of 4 km upstream in 2 hours and the same distance downstream in 20 minutes. How long will it take to go $$10\frac{1}{2}$$ km in still water?

Solution

Let's assume the speed of the boat in still water is B and the speed of the stream is C.

A boat goes a distance of 4 km upstream in 2 hours and the same distance downstream in 20 minutes.

$$\frac{4}{B-C}\ =\ 2$$

B-C = 2 Eq.(i)

$$\frac{4}{B+C}\ =\ \frac{20}{60}$$

$$\frac{4}{B+C}\ =\ \frac{1}{3}$$
B+C = 12 Eq.(ii)
Add Eq.(i) and Eq.(ii),
B-C+B+C = 2+12
2B =14
B = 7 km/h

Time taken to go $$10\frac{1}{2}$$ km in still water = $$\frac{10.5}{7}$$

= 1.5 hours

= $$1\frac{1}{2}$$ hours

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