Question

A boat can travel 9.8 km downstream in 21 mins. The speed of the water current
is 3.5 kmph The boat takes 385 minutes to travel from
point A to B and return to point A. What is the distance between points A and B ? (in km)

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Answer 1

I hope the answer is 124

Answer 2

Therefore the distance between points A and B is 77 Km.

Step-by-step explanation:

A boat can travel 9.8 km in 21 mins

$21 mins =\frac{21}{60} h$

The speed of the boat in downstream = $\frac{9.8}{\frac{21}{60} }$    kmph = 28 Kmph

The speed of the boat in downstream = The speed of boat in still water+ speed of the water current.

$\Rightarrow 28 kmph= \textrm{The speed of boat in still water}+ 3.5 Kmph$

⇒The speed of boat in still water= (28-3.5) kmph

                                                       =24.5  kmph

The speed of the boat in upstream =The speed of boat in still water- speed of the water current.

⇒The speed of the boat in upstream=(24.5-3.5) kmph

                                                             =21 kmph

385 mins $=\frac{385}{60} h$

Let the distance between A to B be x.

The boat travels from A to B and return to point A.

Its mean the boat one time moves with the speed of upstream and another time moves with the speed of downstream.

$Time=\frac{Distance}{speed}$

When the boat travels upstream,

$Time =\frac{x}{21} h$

When the boat travels downstream,

$Time =\frac{x}{28} h$

According to the problem,

$\frac{x}{21} +\frac{x}{28} =\frac{385}{60}$

$\Rightarrow \frac{3x+4x}{84} = \frac{385}{60}$

$\Rightarrow \frac{7x}{84} =\frac{385}{60}$

$\Rightarrow x=\frac{385 \times 84}{7 \times 60}$

⇒x=77

Therefore the distance between points A and B is 77 Km.