A tank is filled by two pipes A and B in 10 hours and 15 hours respectively. If
Practice Questions
Q1
A tank is filled by two pipes A and B in 10 hours and 15 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
4 hours
5 hours
6 hours
7 hours
Questions & Step-by-Step Solutions
A tank is filled by two pipes A and B in 10 hours and 15 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
Step 1: Determine the rate at which pipe A fills the tank. Pipe A fills the tank in 10 hours, so its rate is 1/10 of the tank per hour.
Step 2: Determine the rate at which pipe B fills the tank. Pipe B fills the tank in 15 hours, so its 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 1/10 + 1/15.
Step 4: To add the fractions, find a common denominator. The least common multiple of 10 and 15 is 30.
Step 5: Convert the rates to have the same denominator: 1/10 = 3/30 and 1/15 = 2/30.
Step 6: Now add the two fractions: 3/30 + 2/30 = 5/30.
Step 7: The combined rate of both pipes is 5/30, which simplifies to 1/6 of the tank per hour.
Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of the combined rate: 1 divided by (1/6) equals 6 hours.
Work Rate – Understanding how to calculate the combined work rate of multiple entities working together.
Fraction Addition – Adding fractions with different denominators to find a common rate.
Time Calculation – Calculating the total time taken based on the combined work rate.
