A man can row 50 km upstream and 72 km downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in 12 hours. Find the rate of current.

(1) 3
(2) 8
(3) 4
(4) None of the above


This one is interesting too.

have the feeling that it is last option , none of the above

FOR THOSE OF YOU WHO SOLVED IT, HOW LONG DID IT TAKE YOU?

(STUPID CAPS LOCK)

Yep, the answer is rate = 4



So I suppose you liked the question, huh stoolfi and jay!
stoolfi,
You have the right approach. I solved in the similiar manner too.

I think the hardest part about this problem is having two unknowns as denominators. I think this was of the hard difficulty. I'll pass more like this one as I come cross them. Good job.

A: 50 72 9
B: 70 90 12
X: 20 18 3 (difference b/w A and B)
Y: 80 72 12 (multiply X's with 4)
Z: 60 54 9 (multiply X's data with 3)
W:10 18 (difference b/w Z and A, or Y and B)


From the table, we can conclude that the time to row 10kms upstream = the time to row 18km downstream.

Let that time be k.

(r+c)k = 18
(r-c)k = 10
r = 14/k, c = 4/k

solve for k,
20/(r-c)+18/(r+c) = 3
k = 1.

Answer = c = 4/k = 4/1 = 4

I got the answer in less than 30 secs without writing down a word. Since you are looking for faster approaches, let me write down my thought:

First thing that came to mind was 50/U + 72/D = 9
where U is the upstream speed, D is the downstream speed and D is obviously greater than U.
Now I thought of splitting 9 hrs into 5 hrs and 4 hrs. Why? There was a 50. 5 hrs was screaming out at me and then the remaining would be 4 hrs and 72 is divisible by 4, I know.
If I say that perhaps the time taken to go upstream was 5 hrs, the upstream speed, U, will be 10 km/hr.
If time taken to go downstream is 4 hrs, the downstream speed will be 72/4 = 18 km/hr
Now I need to check if U is actually 10 and D is actually 18. How?
I put it in the other equation.
70/U + 90/D = 12
70/10 + 90/18 = 12
7 + 5 = 12
These values of U and D satisfy.

So difference of speeds of boat and stream is 10 and sum of the speeds is 18.
This would give us two equations: B - S = 10 and B + S = 18
2B = 28
B = 14
So S = 4

GMAT does not require long calculations. If you find yourself making and solving tedious equations, be rest assured that the numbers will fall into place. The 9 hrs given above will not split into 5.2 and 3.8 hrs. It will split into 5 and 4 or 6 and 3 etc. You can pretty much guess the correct answer in the first go by looking at the numerator. 50 is not divisible by 6 but it is divisible by 5. And mind you, all this can be easily done orally. Try to minimize your use of pen and paper; your speed will automatically increase.
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We got U = 10 and D = 18 i.e. Upstream speed = 10 and Downstream Speed = 18
What do you mean by Upstream speed? It means the speed of the boat while going upstream i.e. against the flow of water. Upstream speed is given by Speed of Boat - Speed of stream i.e. the boat loses some speed because it is going against the stream of water. U = B - S

What do you mean by downstream speed? It means the speed of the boat while going downstream i.e. with the flow of the water. Downstream speed is given by Speed of Boat + Speed of stream i.e. the overall speed of the boat increases because the stream is flowing in the same direction and adds to the speed of the boat. D = B + S
_________________

Karishma
Veritas Prep | GMAT Instructor
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