Question

A boat covers a certain distance between two spots in a river taking $t_1$ hrs going downstream and $t_2$ hrs going upstream. What time will be taken by boat to cover same distance in still water ?

• A. $\frac{t_1+t_2}{2}$
• B. $2(t_2=t_1)$
• C. $\frac{2t_1{t}_2}{t_1+t_2}$
• D. $\sqrt{t_1{t}_2}$

Answer 1

The correct option is C $\frac{2t_1{t}_2}{t_1+t_2}$

Let velocity of water be u and velocity of boat in still water be v

Let distance travelled 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)] t₁

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)