Question 15 of 17advanced🔧 ApplyNumerical4 marks

A small pump can fill a tank in 3 hours, while a large pump can fill the same tank in 2 hours. If both pumps are used together, how long will the tank take to fill?

Correct Answer

Step 1: Find rate of small pump: 1 tank ÷ 3 hours = 1/3 tank per hour

Step 2: Find rate of large pump: 1 tank ÷ 2 hours = 1/2 tank per hour

Step 3: Find combined rate: 1/3 + 1/2 = 2/6 + 3/6 = 5/6 tank per hour

Step 4: Calculate time to fill: 1 ÷ (5/6) = 6/5 = 1.2 hours = 1 hour 12 minutes

Answer: The tank will take 1.2 hours (or 1 hour 12 minutes) to fill when both pumps are used together.

Exercise: Figure it Out (Section 4) | Q: 10 | (Page Page 15)
For More Understanding

Explanation

The chapter demonstrates combined work problems. Small pump rate = 1/3 tank per hour. Large pump rate = 1/2 tank per hour. Combined rate = 1/3 + 1/2 = 5/6 tank per hour. Time = 1 ÷ (5/6) = 6/5 = 1.2 hours.

Solution Steps

  1. Step 1: Find rate of small pump: 1 tank ÷ 3 hours = 1/3 tank per hour

  2. Step 2: Find rate of large pump: 1 tank ÷ 2 hours = 1/2 tank per hour

  3. Step 3: Find combined rate: 1/3 + 1/2 = 2/6 + 3/6 = 5/6 tank per hour

  4. Step 4: Calculate time to fill: 1 ÷ (5/6) = 6/5 = 1.2 hours = 1 hour 12 minutes

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