A tank is filled by two pipes in 15 and 20 minutes respectively. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 8.57 minutes
- Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 15 minutes, so its rate is 1/15 of the tank per minute.
- Step 2: The second pipe fills the tank in 20 minutes, so its rate is 1/20 of the tank per minute.
- Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/15 + 1/20.
- Step 4: To add the fractions, find a common denominator. The least common multiple of 15 and 20 is 60.
- Step 5: Convert the fractions: 1/15 becomes 4/60 and 1/20 becomes 3/60.
- Step 6: Now add the two fractions: 4/60 + 3/60 = 7/60.
- Step 7: The combined rate of both pipes is 7/60 of the tank per minute.
- Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of the combined rate: 1 / (7/60) = 60/7 minutes.
- Step 9: Calculate 60/7, which is approximately 8.57 minutes.
- Rate of Work – Understanding how to calculate the combined work rate of multiple entities working together.
- Time Calculation – Applying the formula for time based on the combined rate of work to find the total time taken.
