MATH QUESTION

Discus: SAT/ACT Tests and Test Preparation: May 2003 Archive: MATH QUESTION
 By Coloprisco19 (Coloprisco19) on Saturday, May 31, 2003 - 01:13 am: Edit

pump A working alone can fill a swimming pool in 6 hours. Either of pumps B or C working alone can fill the swimming pool in 3 hours. If all three pumps, working at these rates, are used at the same time to fill the pool, what fraction of the pool is filled by pump A.

please show your work so i can see how u solved the problem

thanx

 By Coloprisco19 (Coloprisco19) on Saturday, May 31, 2003 - 01:41 am: Edit

bump.. anyone know??

 By Dschnapps (Dschnapps) on Saturday, May 31, 2003 - 02:07 am: Edit

the way I'd do it, not sure if you'll understand it but I'd say

(1/6)x + (1/3)x + (1/3)x = 1

x= time

solve for x, x = 6/5

plug that into the 1/6 phrase and you get 6/30
which equals 1/5, so 1/5 is the fraction of the pool filled by A.

Which makes sense considering that B and C go twice as fast so should be responsible for twice as much (1/5 + 2/5 + 2/5 = 1 full pool)

 By Quarky (Quarky) on Saturday, May 31, 2003 - 09:21 am: Edit

That's right. If you want the full version to understand why it works like that.. you got it!

Speed=distance/time

Time: A=6hrs, B=3hrs, C=3hrs
Distance: A=x, B=x, C=x (some unknown volume of the pool)
Speed: A=x/6, B=x/3, C=x/3

When they work together, their total speed is
x/6+2x/3 = 5x/6

So that speed*some time, t = gets the job done (the job of filling the pool, x)

5x/6*t = x
5/6*t = 1
t = 6/5

So the time they spent working together to fill the pool is 6/5 hours.

Thus, pump A during that time period filled this much:
distance=time*speed = 6/5hrs*x/6 = x/5 = 1/5*x
So 1/5 of the total volume of the pool.