A boat covers certain distane between twospots in a river taking t 1 hours going downstream and t 2 hours going upstream. What time will be taken by the boat to cover same distance in still water? Since I am unable to type all the options, pleace give the answers in terms of t 1 and t 2 .

							
Let velocity of water be u and velocity of boat in still water be v
Let distance traveled be d
We need to find d/v
t1= d/(v+u)
d= t1 v + t1 u (1)
t2= d/(v-u)
d = t2 v- t2 u (2)
From 1&2
v t1 + u t1= v t2- u t2
u(t1+ t2) = v(t2- t1)
u = v(t2-t1) / (t1+t2)
Substituting value of u in (1)
d = t1v + t1 [v(t2-t1) /t1+t2)]
d(t1+t2) = t1v(t1+t2) + vt1 (t2-t1)
d(t1+t2) = t1vt1 + t2t1v + vt1t2 - t1t1v
d(t1+t2) =2vt1t2
d/v = 2t1t2/( t1+t2)
Here d/v represents time taken by boat to cover a distance of d in still water
 
						

							
Dear student 
Here is the another method
Suppose a boat is traveling at a constant speed v (without a current), and the current's speed is u
Vup = v+u 
Vdown = v-u 
v = s/t 
v+u = s/t1 
v -u = s/t2 
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 = s/t1 -v 
u = v-s/t2
s/t1 -v = v - s/t2
2v = s/t1 +s/t2
Here, the speed v is the speed of the boat without the current, and is thus equal to
v = s/t(still)
2s/t(still) = s/t1 + s/t2
t(still) = 2t1t2 / (t1+t2)