Ganesh Ujwal

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?

Denis

Makes no sense...do you mean "and 36 km downstream"?

skipjack

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.

Denis

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.

Ganesh Ujwal

What does "................" denote?

Denis

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 ">".