Question

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.

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Answer 1

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Step by step solution:

$Let \ the \ speed \ of \ the \ stream \ be = a \ km/hr\\\\let \ the \ speed \ of \ the \ boat \ be = b \ km/hr\\\\speed \ upstream \ will \ be \ = a-b \ km/hr\\\\ speed \ downstream \ will \ be \ =a+b \ km/hr$

$30 \ km \ upstream \ in \ time \ duration =\frac{30}{a-b} \ hrs\\\\44 \ km \ down \ stream \ in \ time \ duration= \frac{44}{a+b} \ hrs\\\\A.T.Q. \\\\\ \frac{44}{a+b} +\frac{30}{a-b} = 10 \ hrs \ --- (i)\\\\In \ the \ same \ way,$

$\frac{40}{a-b}+\frac{55}{a+b}=13 \ hrs \ Multiply \ with \ \frac{3}{4}\\\\\frac{30}{a-b}+\frac{165}{4(a-b)}=\frac{39}{4} \ ...(ii)\\\\From \ (i) \ and \ (ii) \ we \ get\\\\a+b=11 \ ...(ii)Substitute \ this \ in \ (i) \ we \ get\\\\a-b= 5 \ ...(iv)$

$Now \ we \ have \ (a-b)=5 \ and \ (a+b)=11\\\\From \ this \ we \ get\\\\a=8 \ and \ b=3$

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Answer 2

please refer to the attachment.