Answer:
- It would take them 4.8 minutes if they worked together.
Step-by-step explanation:
The rates of work are additive. That is, <em>the total rate when Anjali and Shayna work together is equal to the sum of the individual rates when they work separetely</em>.
1. <u>Rate of work of Anjali</u>:
- Eight minutes to wax a floor: r₁ = 1 floor / 8 minutes = 1/8
2. <u>Rate of work of Shayna</u>:
- Twelve minutes to was the same floor: r₂ = 1 floor / 12 minutes = 1/12
3. <u>Rate of work if they worked together</u>:
- 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. <u>Time to wax a floor if they worked together</u>
- 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.
