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Expert: - 7/12/2009


Question
22. y/y+2 – 2/ y+3= 10/ y^2+y-6  

a) y= -2 or 3     b) y=0 or -2   
c) y= 2 or -3     d) not given   

24. Tim paddles his kayak 12 km upstream against a 3km/h current and back again in 5 hours and 20 minutes. In that time, how far could he have paddled in still water?   

a) 6 km     c) 1.5 km  
b) 32 km    d) 24 km

Answer
22. I'll assume the problem is really
y/(y+2) - 2/(y+3) = 10/(y²+y-6).

It can be seen that y²+y-6 factors into (y-3)(y+2).

This means that all of the factors found in the denominators are
(y+2), (y+3), and (y-3).

Multiply every term by all three of those factors.

You get y(y+3)(y-3) - 2(y+2)(y-3) = 10(y+3).

Multiplying this out gives y(y²-9) - 2(y²-y-6) = 10(y+3).

Further multiplication gives y^3 - 9y - 2y² + 2y + 12 = 10y + 30.

Putting all of the y terms on one side gives
y^3 - 2y² - 17y - 18...............


Now that was all well and good, but the best thing to do is look at the choices given for the problem.

For (a), if y = -2, y+2 = 0, and that is in the denominator of the first fraction, so it won't work.

For (b), if y = -3, the is a y+3 in the denominator of the second fraction, so it won't work.

For (c), if y = 2, there is a y-2 in the denominator of the right fraction since the bottom, as said, was (y-2)(y+3), so that won't work.

The only choice left is (d).


24. Since we subtract 3km/h going upstream and add 3km/h going downstream, they cancel, and the result is the same as still water.
Since he went 12 km upstream and 12 km downstream, he went a total of 24 km.  That is the same distance he could have gone in still water.  Looking at the responses, I see 24 as being there.

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