Question

A boat goes 30km upstream and 44km downstream in 10 hours. It goes 40 km upstream and 55 km downstream in 13 hours. The speed of the boat in still water is​

Answer 1

Answer:

30+40...70km

40+50...90km

Answer 2

SOLUTION

Let the speed of the boat be x & the speed of the stream be y

The speed of the boat in Upstream=

(x-y)kmph

The speed of the boat in downstream=

(x+y)kmph

Then 30/(x-y) +44/(x+y) = 10

Let 1/(x-y)= a & 1/(x+y)= b

It Implies 30a+44b= 10........(1)

Similarly, 40a+55b= 13........(2)

Multiplying (1) by 4 & (2) by 3, we get

120a+176b=40.......(3)

120+ 165b= 39.......(4)

Subtracting (4) from(3), we get

=) 11b= 1

=) Hence, b= 1/11

Putting b in equation (1), we get

=) 30a+44(1/11)=10

=) 30a +4= 10

=) 30a= 10-4

=) a= 6/30

=) a= 1/5

Now,

b= 1/(x+y) = 1/11

=) x+y= 11..........(5)

and a= 1/(x-y)= 1/5

=) x-y= 5..........(6)

Adding (5) &(6), we get

=) 2x= 16

=)x= 16/2

=) x= 8

Putting x in equation (5), we get

=) 8+y= 11

=) y=11-8

=) y= 3

Hence,the speed of the boat= 8kmph

& speed of the stream= 3kmph

hope it helps ☺️