Question

Can you help explain why this equation is set up this way? I have the equation for a word problem

Answer 1

This is the word problem: Pipe a fills a pool in 5 hours and pipe b fills it in 8 hours. The drain empties the pool in 10 hours. If both pipes are turned on and then 45 minutes later the drain is opened, how long will it take to fill the pool form when the pipes were turned on?

Answer 2

The answer is x/5+x/8-(x/10-3/40)=1

Answer 3

Can you explain why is equation is set up this way? @dan815 @phi

Answer 4

@zepdrix

Answer 5

I start with the idea that
rate * time = amount

Answer 6

Using that rate*time = amount idea,
I try to figure out the "rate"
For example,
Pipe a fills a pool in 5 hours

I translate that into rate= 1 pool/5 hours
if we use that rate then in 5 hours we would have
1 pool/5 hours * 5 hours = 1 pool
i.e. after filling for 5 hours at that rate we get 1 full pool.

What is the rate for pipe B ?

Answer 7

Pipe B would take 1/8 or x/8 and the 1/10 to drain x/10

Answer 8

yes the rate for B is 1/8 (1 pool/ 8 hours) if we put in the units

x is the unknown time in hours

if we fill the pool for x hours and use both pipes the amount going in will be
(1/5)*x + (1/8)*x

ok so far?

Answer 9

yup

Answer 10

I'm confused on the x/10-3/40 part. I don't know how they got 3/40

Answer 11

at the same time water is going in, it is draining out at a rate of 1/10
but we don't start draining until 45 minutes after we start filling
we change 45 minutes to 3/4 hour
the time it is draining is (x- 3/4)
ok ?

Answer 12

yup Im following

Answer 13

rate * time for draining is
1/10* (x-3/4)
if you distribute the 1/10 you get x/10 - 3/40

Answer 14

of course draining means we use -1/10 for the rate, not +1/10
so the equation is

x/5+x/8 - x/10 + 3/40 = 1 (pool)

Answer 15

Thanks for the step by step approach!!

Answer 16

yw