sk818020 wrote:I'm just going to throw in another way of thinking about the problem. Maybe it will help you.
The first sentence states, "Two water pumps, working simultaneously at their respective constant rates, took exactly 4 hours to fill a certain swimming pool."
Mathematically this can be expressed as:
(1/x) + (1/y) = 1/4
Logically we can think of this as Pump X completes 1 unit per every x hours (1/x). Pump Y completes 1 unit every y hours. Together the pumps complete 1 unit every 4 hours. If we can figure out what y is, then we know how long it takes Pump Y to complete 1 job.
Next, "the constant rate of one pump was 1.5 times the constant rate of the other."
In this problem we will say Pump Y is the faster pump, so the amount of time it takes Pump X to complete the job (x) is 1.5 times greater than Pump Y. Or mathematically;
x=1.5y
With this information we can solve the problem by substitution. We want to solve for y so we will substitute 1.5y for any x we see. Thus,
(1/1.5y) + (1/y) = (1/4)
To get rid of all the fractions multiply the entire equation by (1.5y)(y)(4), resulting in:
4y + 6y = (1.5y)y ***see note at bottom.
Divide all terms by y to get;
4 + 6 = 1.5y
Simplify;
10=1.5y
10/1.5 = y
y = 20/3
Therefore, Pump y completes 1 job every 20/3 hours (ratio expressed mathematically as 1/y or 1/(20/3).
Hope that helps some.
Thanks,
Jared
*** You want to be careful not to devide variables because they may be 0, but in this problem we know that one pump is working at 1.5 times the rate of another pump, which wouldn't make sense if either number was 0. Thus, i felt it was safe to devide the variable y here.
Jared,
a good one!
speaking of different approaches, here's one from me. Hope you like it.
I think there is a reason to give the faster rate as 1.5 times the other one. Why?
let the slower rate be x , so the other one becomes 1.5x. combined rate 2.5x which is given to be 1/4 or .25 . See?
therefore , x is .1 and the faster is .15 or 15/100 .
The times is the inverse of this figure or 100/15.
