Question

A boat goes 24km upstream and 28 km downstream in 6 hours it goes 30 km upstream and 21 km down stream in 6 1/2 hours find the speed of the boats on still water and also speed of the stream

Answer 1

Speed of boat in still water is 10kmph
speed of stream is 4kmph

Answer 2

Answer:

The speed of boat in still water is 10 km/hr and the speed of stream is 4 km/hr

Step-by-step explanation:

Given :  A boat goes 24km upstream and 28 km downstream in 6 hours it goes 30 km upstream and 21 km down stream in 6 1/2 hours

To find : Find the speed of the boats on still water and also speed of the stream

Solution

Let the speed of boat in still water be x

Let the speed of stream be y

Upstream Speed = x-y

Downstream speed = x+y

Part A)

Distance of upstream = 24 km

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

$Time = \frac{24}{x-y}$

Distance of down stream  = 28 km

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

$Time = \frac{28}{x+y}$

Since we are given that total time is 6 hours  

So, $\frac{24}{x-y}+\frac{28}{x+y}=6$  ---A

Part B)

Distance of upstream =30 km

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

$Time = \frac{30}{x-y}$

Distance of down stream  = 21 km

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

$Time = \frac{21}{x+y}$

Since we are given that total time is 13/2 hours  

So,$\frac{30}{x-y}+\frac{21}{x+y}=\frac{13}{2}$---B

Solve A and B

$\frac{24}{x-y}+\frac{28}{x+y}=6$

$\frac{30}{x-y}+\frac{21}{x+y}=\frac{13}{2}$

Let $\frac{1}{x-y} = u$ and $\frac{1}{x+y} =v$

So, $24u+28v=6$----1

$30u+21v=\frac{13}{2}$  ---2

Multiply 1 with 5 and 2 with 4

$120u+140v=30$---5

$120u+84v=26$ ---6

Subtract 6 from 5

$120u+140v-120u-84v=30-26$

$140v-84v=4$

$56v=4$

$v=\frac{4}{56}=\frac{1}{14}$

Substitute the value of v in 5

$120u+140(\frac{1}{14})=30$

$120u+10=30$

$120u=20$

$u=\frac{20}{120} =\frac{1}{6}$

So, $\frac{1}{x-y} = \frac{1}{6}$and$\frac{1}{x+y} =\frac{1}{14}$

$x-y=6$--- 7 and$x+y=14$---8

Add 7 and 8

$x-y+x+y=6+14$

$2x=20$

x=10

Substitute in 8  

$10+y=14$

y=4

Hence the speed of boat in still water is 10 km/hr and the speed of stream is 4 km/hr