Expert: Steve Holleran - 10/8/2007

Question
                Data  Sufficiency
Please say whether the information in 1) and/ or
2)is enough to answer the question and provide solutions.

1)If it takes 3 1/2 hours for Matthew to row a distance of x km up the stream. Find his speed in still water.
1)It takes him 2 1/2 hours to cover the distance x km downstream.
2)He can cover a distance of 84 km downstream in 6 hours.

2)A man mixes two types of glues x and y and sells the mixture of x and y at the rate of $17 pr kg. Find his profit percentage.
1)The rate of x is $20 pr kg
2)The rate of y is $13 pr kg

Answer
Hi Andrea,

1)  Well, #1 alone is not enough.  You will still not know the speed of the stream itself.  You can set up these equations:

Let s = Matt's speed in still water
   c = speed of the current
Then you have
Downstream:   (s + c) * 2.5 = x      (rate * time = dist)
Upstream:     (s - c) * 3.5 = x

Setting them =, 2.5s + 2.5c = 3.5s - 3.5c
                        6c = 1s

and you don't have enough info.

With the addtion of #2, then downstream you have

            84 = R * 6   so R = 14, so now you know

       s + c = 14  and s = 6c, so 6c + c = 14 and c = 2.

Then s = 6 * 2 = 12.


2)  I don't see anything here about cost in either case.  If the question is about profit percentage, you have to have some cost information, or you cannot figure any type of profit.  

Hope this helps out.
Steve