Question

If a boatman rows his boat 35km up stream and 55km downstream in 12 hours and he can row 30km upstream and 44 km downstream in 10hr , then the speed of the stream and that of the boat in still water

Answer 1

speed of the stream = 3 km/hr

and speed of boat in still water= 8 km/hr

Explanation:

Let s be the speed of the boat upstream

and s' be the speed of the boat downstream.

We know that:

`Time=(distance)/(speed)`

Hence, we get:

`(35)/(s)+(55)/(s')=12`

and

`(30)/(s)+(44)/(s')=10`

Now, let

`(1)/(s)=a\ and\ (1)/(s')=b`

Hence, we have:

`35a+55b=12--------------(1)\\\\\\and\\\\\\30a+44b=10--------------(2)`

on multiplying equation (1) by 4 and equation (2) by 5 and subtract equation (1) from (2) we get:

`a=(1)/(5)`

and by putting value of a in (2) we get:

`b=(1)/(11)`

Hence, speed of boat in upstream= 5 km/hr

and speed of boat in downstream= 11 km/hr

and we know that:

speed of boat in upstream=speed of boat in still water(x)-speed of stream(y)

and speed of boat in downstream=speed of boat in still water(x)+speed of stream(y)

Hence, we get:

`x-y=5\\\\\\and\\\\\\x+y=11`

Hence, on solving the equation we get:

`x=8`

and y=3

Hence, we get:

speed of the stream = 3 km/hr

and speed of boat in still water= 8 km/hr

Answer 2

To answer this item, we let x be the speed of the boat in still water. The speed of the current, we represent as y.

When the boat travels upstream or against the current, the speed is equal to x – y and x + y if it travels downstream or along with the current.

The time it takes for the an object to travel a certain distance is calculated by dividing the distance by the speed.

First Travel: 35 / (x – y) + 55 / (x + y) = 12

Second travel: 30 / (x – y) + 44 / (x + y) = 10

Let us multiply the two equations with the (x-y)(x+y)

This will give us,

35(x + y) + 55(x – y) = 12(x-y)(x+y)

30(x + y) + 44(x – y) = 10(x-y)(x+y)

Using dummy variables:

Let a = x + y and b be x – y

35a + 55b = 12ab

30a + 44b = 10ab

From the first equation,

b = 35a/(12a – 55)

Substituting to the second equation,

30a + 44(35a/(12a – 55)) = 10a(35a/(12a-55))

The value of a is 11.

b = 35(11)/(12(11) – 55))

b = 5

Putting back the equations,

x + y = 11

x – y = 5

Adding up the equations give us,

2x = 16

x = 8 km/hr

The value of x, the speed of the boat in still water, is 8 km/hr.