Question

A person can swim in still water at 5m/s he swims in a river of velocity 3m/s first down the stream next same distance up the stream the ratio of time taken are

Answer 1

Speed of person in still water = 5m/s

Speed of stream = 3m/s

Time = Distance/speed

Let distance be 'x'

Speed in downstream = 5+3 m/s

= 8 m/s

Speed in upstream = 5-3 m/s

= 2 m/s

Time in downstream = x/8 seconds

Time in upstream = x/2 seconds

Therefore,

Ratio of time in downstream to upstream = x/8:x/2

= 1:4 seconds

Answer 2

Answer: The ratio of time taken is 1/4.

Explanation: Here, we need the ratio of time taken to travel the same amount of distance downstream and then upstream.

Let the distance traveled be x:

$V_{m}=5m/s\\V_{r}=3m/s$

Downstream: When the object be it a boat or a person is flowing in the direction of the stream, In this case, net velocity is the sum of both.$V_{downstream}=V_{m}+V_{r}$

Upstream: When the object be it a boat or person flows or swims in the direction opposite to that of the stream, In this case, net velocity is the difference of both.

$V_{upstream}=V_{m}-V_{r}$

$Time\ taken=Distance/Velocity$

(distance is same)

$T_{d}/T_{u}=(x/8)\times (2/x)=1/4$