Question

It takes Anjali eight minutes to wax a floor. Shayna can wax the same floor in 12 minutes. Find how long it would take them if they worked together.

Answer 1

• It would take them 4.8 minutes if they worked together.

Explanation:

The rates of work are additive. That is, the total rate when Anjali and Shayna work together is equal to the sum of the individual rates when they work separetely.

1. Rate of work of Anjali:

• Eight minutes to wax a floor: r₁ = 1 floor / 8 minutes = 1/8

2. Rate of work of Shayna:

• Twelve minutes to was the same floor: r₂ = 1 floor / 12 minutes = 1/12

3. Rate of work if they worked together:

• r = r₁ + r₂ = 1/8 + 1/12
• steps to add the fractions:

- least common denominator: 2³ · 3 = 24

- r = 1/8 + 1/12 = 3/24 + 2/24 = 5/24 = 0.2083 ...

- that mean 5 floors/24 minute = 0.2083... floors/minute

4. Time to wax a floor if they worked together

• The time to wax one floor (minutes per floor) is the inverse of the rate, floors per minute:

- time = 1 / r = 24/5 = 4.8 minutes per floor.