Question 11

A boat travels from A to B upstream and then from B to C downstream taking the same time. The respective ratio between the distance from A to B and the distance from B to C is 5 : 7. If the boat takes 2 hours 30 min to travel a distance of 35 km downstream, what is the speed of the stream ? (in km/h)

Solution

Let distance between AB = $$5x$$ and BC = $$7x$$

Downstream speed = $$\frac{35}{2.5} = 14$$ km/h

Let upstream speed = $$y$$ km/h

Now, $$time = \frac{distance}{speed}$$

=> $$\frac{5x}{y} = \frac{7x}{14}$$

=> $$\frac{5}{y} = \frac{1}{2}$$

=> $$y = 5 \times 2 = 10$$ km/h

Now, speed of stream = $$\frac{1}{2}$$ (downstream - upstream)

= $$\frac{1}{2} (14 - 10)$$

= $$\frac{4}{2} = 2$$ km/h

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