Question

Aman can row his canoe at 10 km/hr in still water but he takes 4 hrs more to row upstream in comparison to downstream if the distance upstream or downstream is 30 km find the speed of stream​

Answer 1

Answer:

5 km/hr

Step-by-step explanation:

Let the speed of the stream be $v$ km/hr

Speed of the canoe = 10 km/hr

When canoe is going downstream, the net speed of canoe  = $10+v$ km/hr

When canoe is going upstream, the net speed of canoe =  $10-v$ km/hr

Let the time taken in rowing downstream be $t$

Then, $t = \frac{30}{10+v}$   (∵ Time = Distance/Speed)  ........ (i)

Again $t+4 = \frac{30}{10-v}$                                              ..........(ii)

Subtracting equation (i) from equation (ii) we get

$4 = \frac{30}{10-v} -\frac{30}{10+v}$

or, $\frac{4}{30} = \frac{1}{10-v} -\frac{1}{10+v}$

or, $\frac{2}{15} = \frac{10+v-10+v}{(10-v)(10+v)}$

or, $\frac{1}{15}= \frac{v}{100-v^{2} }$

or, $100-v^{2} = 15v$

or, $v^{2} +15v-100=0$

or, $v^{2} +20v-5v-100=0$

or, $v(v+20)-5(v+20) = 0$

or, $(v+20)(v-5) = 0$

this gives, $v=-20$ or $5$

but speed cannot be negative

∴ $v = 5$

Thus the speed of the stream  = 5 km/hr

Answer 2

Answer:

Step-by-step explanation:

Our question is: Aman can row his canoe at 10 km/hr in still water but he takes 4 hrs more to row upstream in comparison to downstream if the distance upstream or downstream is 30 km.

Our aim is to find the speed of stream​.

In order to reach our aim, lets consider v to be the aditional speed of Aman's canoe when downstream.

Thus, when going downstream, the speed of the canoe is equal to 10 + v.

Otherwise, when canoe is going upstream, the speed of the canoe is equal to 10 - v.

Lets use time in order to get our answer.

Let t, be the time, in hours, taken when going downstream.

Thus t = 30 : (10 - v), and t + 4 = 30 : (10 + v)

Substituting t in the second equation we have v = -20 or v = 5.

Since, speed can not be negative we can conclude that v = 5.

Hence, the speed of the canoe is equal to 5 km/hr.

I hope this helps your studies!

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