A tank can be filled by two pipes in 12 hours and 15 hours respectively. How lon
Practice Questions
Q1
A tank can be filled by two pipes in 12 hours and 15 hours respectively. How long will it take to fill the tank if both pipes are opened together? (2021)
7 hours
8 hours
9 hours
10 hours
Questions & Step-by-Step Solutions
A tank can be filled by two pipes in 12 hours and 15 hours respectively. How long will it take to fill the tank if both pipes are opened together? (2021)
Step 1: Determine the rate at which the first pipe fills the tank. Since it takes 12 hours to fill the tank, the rate is 1/12 of the tank per hour.
Step 2: Determine the rate at which the second pipe fills the tank. Since it takes 15 hours to fill the tank, the rate is 1/15 of the tank per hour.
Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/12 + 1/15.
Step 4: To add 1/12 and 1/15, find a common denominator. The least common multiple of 12 and 15 is 60.
Step 5: Convert 1/12 to 5/60 and 1/15 to 4/60.
Step 6: Now add the two fractions: 5/60 + 4/60 = 9/60.
Step 7: Simplify 9/60 to 3/20. This means the combined rate of both pipes is 3/20 of the tank per hour.
Step 8: To find out how long it takes to fill the tank, take the reciprocal of the combined rate. The reciprocal of 3/20 is 20/3.
Step 9: Calculate 20/3 hours, which is approximately 6.67 hours or 6 hours and 40 minutes.
Work Rate – Understanding how to calculate the rate of work done by each pipe and how to combine these rates.
Fraction Addition – Adding fractions with different denominators to find a common rate.
Time Calculation – Calculating the total time taken to complete a task based on combined work rates.
