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A boat covers certain distane between twospots in a river taking t 1 hours going downstream and t 2 hours going upstream. What time will be taken by the boat to cover same distance in still water? Since I am unable to type all the options, pleace give the answers in terms of t 1 and t 2 .

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6 months ago

```							Let velocity of water be u and velocity of boat in still water be vLet distance traveled be dWe need to find d/vt1= d/(v+u)d= t1 v + t1 u (1)t2= d/(v-u)d = t2 v- t2 u (2)From 1&2v t1 + u t1= v t2- u t2u(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 - t1t1vd(t1+t2) =2vt1t2d/v = 2t1t2/( t1+t2)Here d/v represents time taken by boat to cover a distance of d in still water
```
6 months ago
```							Dear student Here is the another methodSuppose a boat is traveling at a constant speed v (without a current), and the current's speed is uVup = v+u Vdown = v-u v = s/t v+u = s/t1 v -u = s/t2 The quantity u (the current's speed) is constant for both equations, so let's solve both equations for u and set them equal to each otheru = s/t1 -v u = v-s/t2s/t1 -v = v - s/t22v = s/t1 +s/t2Here, the speed v is the speed of the boat without the current, and is thus equal tov = s/t(still)2s/t(still) = s/t1 + s/t2t(still) = 2t1t2 / (t1+t2)
```
6 months ago
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