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A fisherman on a boat sailed against the current of the river, an empty flask fell from the boat into the river near the bridge. After that, having sailed $15$ minutes against the current of the river, the fisherman noticed his loss and swam in the opposite direction to catch up with the flask. What is the speed of the river if the fisherman caught up with the flask $4$ kilometres downstream of the bridge?

$v_1$ - current velocity

$v_2$ is the swimmer's speed

respectively $v_2-v_1$ is the upstream speed, $v_2 + v_1$ downstream after losing the flask, they moved away from each other at a speed $v_1 + v_2 - v_1$, which means in $15$ minutes we parted to $(v_1 + v_2 - v_1) * 15 = s$, $s$ is the final distance between them before the start of the convergence, then they began to converge $(v_2 + v_1 - v_1) * T = s$, $T$ is the approach time, we have

$v_2 * 15 = S$

$v_2 * T = S $

$T = 15$, from where we easily find $v_1 = 8$ km / h

right or wrong?

ryan1
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марат
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    How did you get that answer? – Daniel Hast Nov 19 '20 at 18:58
  • It matters more how you got that answer. Maybe you're right for the wrong reasons; maybe you're wrong for a trivial calculation error. Who knows? – Shaun Nov 19 '20 at 19:06
  • @DanielHast corrected your remark and added a solution – марат Nov 19 '20 at 19:06
  • @Shaun added solution – марат Nov 19 '20 at 19:07
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    The explanation is a little unclear, partly from things like saying "they" without saying who they are, partly from lack of punctuation and formatting, but if we assume the boat sails through the water exactly as fast as the fisherman can swim (big assumption!) you seem to have a correct method and a correct answer. – David K Nov 19 '20 at 19:20
  • @DavidK here one interesting solution appeared, only the answers diverge The flask sailed 4 km in 15 minutes V river = 4 km \ 15 min = 4 km \ (1 \ 4) hours = 16 km \ hour – марат Nov 19 '20 at 20:38
  • @DavidK I found a bug in this solution. The flask swam for those 15 minutes that the fisherman was still swimming against the current, and then some more time that the fisherman spent on the way to the bridge and after the bridge for another 4 km. and then it turns out (4 km) /(0.5 hours) = 8 km / h. – марат Nov 19 '20 at 20:42

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