Rama packs 36 boxes in 1 h. Her sister needs 3 h to pack the same number. How much time will they together take to pack these 36 boxes?

Correct option is D

Given:

Rama packs 36 boxes in 1 hour.

Her sister packs 36 boxes in 3 hours.

Formula Used:

$$\text{Time} = \frac{\text{Total work}}{\text{Combined work rate}}$$​

Solution:

Rama packs 36 boxes in 1 hour.

Rama's work rate is 36 boxes/hour.

Sister packs 36 boxes in 3 hours.

Sister's work rate is $$\frac{36 \text{boxes }} {3 \text{hours}}$$​ = 12 boxes/hour.

Combined work rate = Rama's work rate + Sister's work rate.

Combined work rate = 36 boxes/hour + 12 boxes/hour = 48 boxes/hour.

​$$\text{Time} = \frac{\text{Total work}}{\text{Combined work rate}}$$​​

Time = $$\frac{36 \text{ boxes}}{48 \text{ boxes/hour}}$$​​

Time =$$\frac{ 3}{4 }$$​hours.

Convert to minutes:

​$$\frac{ 3}{4 }$$​ hours $$\times$$​ 60 minutes/hour = 45 minutes.