Question

heya x3 is there anyone good with word problems?? (i'm in algebra 1)

this is one of the problems i have:
If three pipes are all opened, they can fill an empty swimming pool in 3 h. The largest pipe alone takes one third the time that the smallest pipe takes and half the time the other pipe takes. How long would it take each pipe to fill the pool by itself?

Answer 1

3 pipes: take a, b c hrs respectively to fill the pool. a < b< c.
In 1 hr, pipe 1 fills (1/a) fraction of the pool. Similarly in 1 hr, 2nd and 3rd pipes fill (1/b) and (1/c) fraction of the pool.
Thus in 1 hr fraction of the pool that is filled up by all three pipes together: (1/a) + (1/b) + (1/c). This is equal to 1/3 (from the given condition that it takes 3hrs for all the 3pipes to fill the pool)
The other conditions are: b = 2a and c = 3a.

Using these equations you get: a = 5.5hrs b = 11hrs and c = 16.5hrs

Answer 2

pipe 1) 5.5 hours
Pipe 2) 11 hours
Pipe 3) 16.5 hours