if a person can fill a tank in 12 min. and another person can fill a tank in 20 min. How long will it take both of them to fill 1 tank together?
12/60 = 1/5 of an hour
1 tank can be filled in 1/5 of an hour
your rate is 5 tanks per hour
20/60 = 1/3 of an hour
The tank can be filled in 1/3 of an hour. your rate is 3 tanks per hour
(5 tanks per hour)time + (3 tanks per hour)time = 1 tank filled
5t + 3t = 1
t =1/8 of an hour.
This makes sense because it should take less time to fill the tank if both are working together.
To find out how long it will take both people to fill the tank together, we can use the concept of work.
Let's say the capacity of the tank is 1 unit (you can assume any unit you prefer).
Person A can fill the tank in 12 minutes, which means they do 1/12th of the work in 1 minute. Conversely, Person A takes 12 minutes to complete the entire job.
Similarly, Person B can fill the tank in 20 minutes, so they complete 1/20th of the work in 1 minute.
To calculate how long it takes for both of them to fill the tank together, we need to add their individual rates of work. So, we have:
Person A's rate of work = 1/12 per minute
Person B's rate of work = 1/20 per minute
When they work together, we can add their rates:
1/12 + 1/20 = (20 + 12)/(12 × 20) = 32/240 = 4/30 = 1/7.5
Therefore, when working together, they have a combined rate of 1/7.5 per minute. This means they complete 1/7.5th of the work in 1 minute.
To find out how long it takes for them to complete the entire job together, we can take the reciprocal of their combined rate:
1 / (1/7.5) = 7.5
Hence, it will take both of them 7.5 minutes to fill the tank together.