Question

a boat covers certain distance between two spot in a river taking time t 1 hours going downstream and t2 hours going upstream what will be the time taken by the boat to cover the same distance in still water

Answer 1

Explanation:

We're asked to find the expression for the time it takes the boat to travel across the river in still water.

I'll try and show this with a little example:

Suppose a boat is traveling at a constant speed v(without a current), and the current's speed is u

Going upstream, the true speed of the boat would be

vup=v+u

And going downstream, we have

vdown=v−u

We have our general speed equation:

v=st

Or in these two cases

v+u=st1

v−u=st2

(the distance across the river s is constant)

The quantity u (the current's speed) is constant for both equations, so let's solve both equations for u and set them equal to each other:

u=st1−v

u=v−st2

So

st1−v=v−st2

2v=st1+st2

Here, the speed v is the speed of the boat without the current, and is thus equal to

v=ststill:

2ststill=st1+st2

2tstill=1t1+1t2

tstill=21t1+1t2

Get the denominator's fractions into a common denominator:

tstill=2t2+t1t1t2

or


¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯∣∣∣ tstill=2t1t2t1+t2 ∣∣∣−−−−−−−−−−−−−−−−−−