Question

a boat covers certain distance between two spots in a river taking t1 hrs going downstream and t2 hrs going upstream .What time will be taken by boat to cover same distance in still water?

Answer 1

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

Answer 2

Answer:

2t1t2/(t1+t2)

Explanation:

• 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