Question

A man rows directly across a river flowing in time t1 and rows an equal distance down the stream in time t2. If u and v are the speed of the man in still water and speed of stream respectively, then t1²:t2²=u+v:u-v

Answer 1

Knowing that;

Speed=Distance/Time;

Hence,

Time=Distance/Speed

Ratio of t₁ and t₂ is as below:

t₁/t₂=d₁/s₁÷d₂/s₂

As distance is the same for both t₁ and t₂; it would be nullified.

Hence,

t₁/t₂=s₁/s₂

Now speed s₁ is the speed of boat when upstream, i.e the difference of speed of boat in still water and the speed of water

s₁ =u-v m/s and

s₂ is the speed of boat when downstream, i.e the sum of speed of boat in still water and the speed of water

s₂=u+v m/s

Therefore, the ratio of t₁ and t₂ is s₂/ s₁ i.e u+v/u-v.

Answer 2

Answer:s2/s1 i.e. u+v/u-v

Explanation:

Knowing that;

Speed=Distance/Time;

Hence,

Time=Distance/Speed

Ratio of t₁ and t₂ is as below:

t₁/t₂=d₁/s₁÷d₂/s₂

As distance is the same for both t₁ and t₂; it would be nullified.

Hence,

t₁/t₂=s₁/s₂

Now speed s₁ is the speed of boat when upstream, i.e the difference of speed of boat in still water and the speed of water

s₁ =u-v m/s and

s₂ is the speed of boat when downstream, i.e the sum of speed of boat in still water and the speed of water

s₂=u+v m/s

Therefore, the ratio of t₁ and t₂ is s₂/ s₁ i.e u+v/u-v.