One pipe can fill a pool in 10 hours. Another pipe can fill the pool in 30 hours. How long would it take them to fill the pool if they were working together?
rate 1 = R1 = 1 pool/10 hr
R2 = 1 pool/30 hr
together
(1 pool/10 hr) T + (1 pool/30 hr)T = 1 pool
T/10 + T/30 = 1
3 T/30 + 1 T/30 = 1
4 T = 30
T = 7.5 hours
7 hours 30 minutes
7 hours 30 minutes or 7.5 hours
Damon gave a great explanation I'm just restating this in case someone missed his
To find out how long it would take for two pipes to fill the pool working together, we can use the concept of rates.
Let's first find out the rate at which each pipe can fill the pool:
- The first pipe can fill the pool in 10 hours. Therefore, its rate of filling the pool is 1/10 (1 pool filled in 10 hours).
- The second pipe can fill the pool in 30 hours. Therefore, its rate of filling the pool is 1/30 (1 pool filled in 30 hours).
When two pipes are working together, their rates of filling the pool add up:
Rate of first pipe + Rate of second pipe = Combined rate
1/10 + 1/30 = Combined rate
To simplify the calculation, we need to find a common denominator:
1/10 + 1/30 = (3/30) + (1/30) = 4/30
So, the combined rate of the two pipes working together to fill the pool is 4/30, or 2/15 (since both numerator and denominator can be divided by 2).
Now, we can find the time it would take for the two pipes to fill the pool together:
Time = 1 / Combined rate
Time = 1 / (2/15) = 15/2
Therefore, it would take them 7.5 hours, or 7 hours and 30 minutes, to fill the pool if they were working together.
2
One pipe can fill a pool in 9 hours. Another pipe can fill the pool in 6 hours. How long would it take them to fill the pool if they were working together?
Answer