m06 Q19

Question

Hi

A boat crossed a lake from North to South at the speed of 4 km/h, entered a river and covered twice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?

I'm a bit unsure about answer explanation in this, I think the answer is correct but we don't need to calculate anything at all, the question itself gives the answer, here is why :

Speed in lake (which can taken as speed in "still water", as happens in such problems) = 4 km/h and upstream speed = 3 km/h, so speed of river = 4-3 = 1 km/h.

Naturally, downstream speed = speed in "still water" + speed of river = 4 + 1 = 5 km/h

Opinions ?

Regards,
Subhash

subhashghosh · Answer

Also, my calculations are :

If v is the downstream speed :

(x + 2x + 2x)/(x/4 + 2x/3 + 2x/v) = 3.8

=> 5/(1/4 + 2/3 +2/v) = 19/5

=> 5/(11/12 + 2/v) = 19/5

=> 5/(11v + 24)/12v = 19/5

=> 60v/(11v + 24) = 19/5

=> 300v = 209v + 456

=> 91v = 456

=> v = 456/91 = 5.01

subhashghosh · Answer

So this question should be reworded ?

fluke · Answer

Don't think it's necessary. There are multiple ways to solve it, that's all. A smart solver would just choose your former method to solve it.

josephlcs · Answer

I think the assumption that downstream speed = still-water speed + river speed is a big assumption. In this question it so happens that this assumption holds true, but if the question were to change the average speed to something else the question would still be valid, and you would be caught.

It's not very hard to see how this assumption could be wrong in real-life. A boat's speed could adjust differently to upstream and downstream waters because wind resistance is proportional to the square of your speed, meaning that you suffer less resistance at slower speeds than at higher speeds. But the average speed of the whole journey holds true regardless what journey conditions were.

I think it's clever the way you thought about it, but I would still do the mathwork in the real thing, just in case GMAT decides to screw with me. =)

m06 Q19

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