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 August 27th, 2018, 08:25 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 343 Thanks: 1 How to solve this problem in simple way? A boat goes 24 km upstream and 36 km upstream in 8 hours and 30 mins while if it goes 36 km upstream and 24 km downstream, the boat takes 9 hours. What is the speed of the boat in still water? Let c be the current and s be the speed of the boat. t1, t2, t3, and t4 be the times. (c-s)t1 = 24 [takes t1 hours to go upstream 24 km] (c+s)t2 = 36 [takes t2 hours to go downstream 36 km] t1 + t2 = 8.5 [total time is 8.5 hours] (c-s)t3 = 36 (c+s)t4 = 24 t3 + t4 = 9 T1 + T2 = 8.5 $\frac {24}{C - S}$ + $\frac {36}{C + S}$ = 8.5 (24)(C + S) + 36(C - S) = (8.5)($C^2$ - $S^2$) 60 C - 12 S = 8.5 ($C^2$ - $S^2$) It is getting complicated. Do you have any shortcuts to proceed this problem? Last edited by skipjack; August 27th, 2018 at 11:50 AM.
August 27th, 2018, 08:55 AM   #2
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Quote:
 Originally Posted by Ganesh Ujwal A boat goes 24 km upstream and 36 km upstream in 8 hours and 30 mins...
Makes no sense...do you mean "and 36 km downstream"?

August 27th, 2018, 09:45 AM   #3
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Quote:
 Originally Posted by Ganesh Ujwal It is getting complicated.
Accepting the amendment Denis suggested, it's straightforward.
Let p = 1/(c - s) and q = 1/(c + s).
24p + 36q = 8.5 and (similarly) 36p + 24q = 9,
so 48p + 72q = 17 and 108p + 72q = 27.
By subtraction, 60p = 10 and so 72q = 9.
Hence c - s = 1/p = 6 and c + s = 1/q = 8.
Solving is now easy and gives c = 7 and s = 1.
I omitted the units in the above, so the answer is 1 km/h.

 August 27th, 2018, 10:23 AM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,961 Thanks: 991 If you're not too busy or tired, you can always make one up to see how it works, like making boat speed = 25 and current speed = 5. then creating this scenario (as example): A boat goes 120 km downstream and 60 km upstream in 7 hours. Same boat goes 60 km downstream and 120 km upstream in 8 hours. What is the speed of the boat in still water? v = boat speed, c = current speed @v+c................120..................>@v-c........60...........>7 hr @v+c.......60........>@v-c..................120....................>8 hr Now solve that for v: you should get v=25. Thanks from topsquark
August 27th, 2018, 08:38 PM   #5
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Quote:
 Originally Posted by Denis v = boat speed, c = current speed @v+c................120..................>@v-c........60...........>7 hr @v+c.......60........>@v-c..................120....................>8 hr Now solve that for v: you should get v=25.
What does "................" denote?

 August 28th, 2018, 04:52 AM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,961 Thanks: 991 Represents a path, like river or road... @v+c................120..................>@v-c........60...........>7 hr Here, represents the river, 180 total length, travelled from left to right, as indicated with ">".

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