Question

A motorboat goes downstream on a river and covers a distance between two towns in 6 hours it covers the distance upstream in a 8 hours if the speed of the stream is 2 km per hour find the distance between two towns will be​

Answer 1

Answer:

120 km

Step-by-step explanation:

Since we have to find the speed of the boat in still water, let us suppose that it is x km/h.

This means that while going downstream the speed of the boat will be (x+2) kmph because the water current is pushing the boat at 2 kmph in addition to its own speed 'x' kmph.

Now the speed of the boat down stream =(x+2) kmph

⇒ distance covered in 1 hour =x+2 km

∴ distance covered in 5 hours =5(x+2) km

Hence the distance between A and B is 5(x+2)km

But while going upstream the boat has to work against the water current.

Therefore its speed upstream will be (x−2) kmph.

⇒ Distance covered in 1 hour =(x−2) km

Distance covered in 6 hours =6(x−2) km

∴ distance between A and B is 6(x−2) km

But the distance between A and B is fixed

∴ 5(x+2)=6(x−2)

⇒ 5x+10=−12−10

∴ −x=−22

x=22

⇒ distance between A and B is 5(x+2)km

=5(22+2)

=5(24)

=120 km

=answer

Answer 2

Answer is 96km

let the distance between two town be y

and the speed of the boat in water be x

A/Q

speed Of the boat in downstream=x+2

speed of the boat in upstream =x‐2

so,distance=speed×time

for downstream

(x+2)×6 = y

6x+12=y

6x-y=-12...eq i

for upstream

(x‐2)×8 =y

8x‐16=y

8x‐y=16...eq ii

Now subtracting eq i and ii

8x-y=16

6x‐y=‐12

2x=28

x=14km/hr

Now putting the value of x in eq ii

8×14‐y=16

112‐y=16

‐y≈16‐112

y=96km

check

speed of downstream=x+2=14+2≈16

time=6hr

distance=16×6=96 proved