Question

A Boat went down the river for a distance of 10km. it then turned back and returned to its starting point, having travelled a total hours. o its return trip, at a distance of 6 km from the starting point, it encountered a block of wood, which had passed the starting point at the moment at which boat had started downstream. what was the downstream speed of the boad?

Answer 1

Step-by-step explanation:

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Answer 2

Disclaimer:

Total time is taken as 5 hours.

Concept:

Speed can be defined as the distance traveled per unit of time.

Given:

The distance traveled on went down the trip is 10 km. On the return trip, the distance traveled from the starting point is 6 km.

Find:

The downstream speed of the boat.

Solution:

Take x to be the speed of the water in the still water and y to be the speed of the stream.

So, the upstream speed of the boat is x-y and the downstream speed of the boat is x+y.

The time is taken by the boat in traveling,

$\frac{4}{y}=\frac{10}{x+y}+\frac{6}{x-y}$

On reducing equations,

$\frac{x}{y}=4$

So, we can take any proportionality constant, a,

So, x=4a and y=a

Also, here, it traveled a total of 5 hours.

Substituting the values of x and y,

$5=\frac{10}{x+y}+\frac{10}{x-y}$

$5=\frac{10}{5a}+\frac{10}{3a}$

So, a=16/15

Now, solving the equations, x+y as x+y is the downstream speed of boat,

x + y = 4a+a = 5a

x + y = $\frac{16}{3}$ km/h

Hence, the downstream speed of the boat is $\frac{16}{3}$ km/h.

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