Can you help explain why this equation is set up this way? I have the equation for a word problem
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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?
The answer is x/5+x/8-(x/10-3/40)=1
Can you explain why is equation is set up this way? @dan815 @phi
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I start with the idea that
rate * time = amount
Using that rate*time = amount idea,
I try to figure out the "rate"
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 ?
Pipe B would take 1/8 or x/8 and the 1/10 to drain x/10
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?
I'm confused on the x/10-3/40 part. I don't know how they got 3/40
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)
yup Im following
rate * time for draining is
if you distribute the 1/10 you get x/10 - 3/40
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)