Respuesta :
We have to find how much time will be consumed if both John and Matt fill the pool together and show the steps to reach at the answer.
Solution:
John fill the pool in 5 hours. This means in 1 hour John fills [tex] \frac{1}{5} [/tex] part of the pool. Matt fills the pool in 10 hours. This means in 1 hour Matt fill [tex] \frac{1}{10} [/tex] part of the pool.
If they both work together:
Portion of the pool filled in 1 hour = [tex] \frac{1}{5}+ \frac{1}{10}= \frac{3}{10} [/tex]
Next we can use proportion to solve this problem.
3/10 portion of the pool is filled in 1 hour.
3/10 of the pool is filled in time ⇒ 1 hour
Multiplying both sides by 10/3 we get
3/10 x 10/3 of the pool in time = 1 x 10/3
1 pool is filled in time = 10/3 hours
This means, if both John and Matt fill the pool together they will take 10/3 hours which is 3 hours and 20 minutes to fill the pool.
A shortcut to solve such questions is:
Time taken to fill the pool = (Product of individual times)/(Sum of individual times)
Time taken to fill the pool = [tex] \frac{5(10)}{5+10}= \frac{50}{15}= \frac{10}{3} [/tex]
This results in the same answer as we achieved above.
Solution:
John fill the pool in 5 hours. This means in 1 hour John fills [tex] \frac{1}{5} [/tex] part of the pool. Matt fills the pool in 10 hours. This means in 1 hour Matt fill [tex] \frac{1}{10} [/tex] part of the pool.
If they both work together:
Portion of the pool filled in 1 hour = [tex] \frac{1}{5}+ \frac{1}{10}= \frac{3}{10} [/tex]
Next we can use proportion to solve this problem.
3/10 portion of the pool is filled in 1 hour.
3/10 of the pool is filled in time ⇒ 1 hour
Multiplying both sides by 10/3 we get
3/10 x 10/3 of the pool in time = 1 x 10/3
1 pool is filled in time = 10/3 hours
This means, if both John and Matt fill the pool together they will take 10/3 hours which is 3 hours and 20 minutes to fill the pool.
A shortcut to solve such questions is:
Time taken to fill the pool = (Product of individual times)/(Sum of individual times)
Time taken to fill the pool = [tex] \frac{5(10)}{5+10}= \frac{50}{15}= \frac{10}{3} [/tex]
This results in the same answer as we achieved above.
