A pipe can fill a tank in 5 hours, and a second pipe can fill the same tank in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
Practice Questions
1 question
Q1
A pipe can fill a tank in 5 hours, and a second pipe can fill the same tank in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
2 hours
3 hours
4 hours
5 hours
The combined rate is 1/5 + 1/10 = 3/10. Therefore, it will take 10/3 hours or 3.33 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: A pipe can fill a tank in 5 hours, and a second pipe can fill the same tank in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The combined rate is 1/5 + 1/10 = 3/10. Therefore, it will take 10/3 hours or 3.33 hours to fill the tank.
Steps: 8
Step 1: Determine the rate at which the first pipe fills the tank. Since it can fill the tank in 5 hours, its rate is 1 tank per 5 hours, or 1/5 of the tank per hour.
Step 2: Determine the rate at which the second pipe fills the tank. Since it can fill the tank in 10 hours, its rate is 1 tank per 10 hours, or 1/10 of the tank per hour.
Step 3: Add the rates of both pipes together to find the combined rate. This is 1/5 + 1/10.
Step 4: To add 1/5 and 1/10, find a common denominator. The common denominator for 5 and 10 is 10. Convert 1/5 to 2/10.
Step 5: Now add the two fractions: 2/10 + 1/10 = 3/10.
Step 6: The combined rate of both pipes is 3/10 of the tank per hour. This means together they fill 3/10 of the tank in one hour.
Step 7: To find out how long it takes to fill the entire tank, take the reciprocal of the combined rate. The reciprocal of 3/10 is 10/3 hours.
Step 8: Convert 10/3 hours into a more understandable format. 10/3 hours is approximately 3.33 hours.
