Answer:
Total time = 63 hours
Step-by-step explanation:
First, let us write out the information in the question:
rate at which rooms are cleaned = 20 mins/room
number of rooms = 175
one-fifth of the rooms take 40% longer to clean
Next, let us convert the extra time taken to clean the rooms from percentage to time.
40% of normal cleaning time = 40% of 20
= 40/100 × 20 = 0.4 × 20 = 8 minutes
∴ onw-fifth of the rooms take an extra 8 minutes = 28 minutes in total
Next, let us calculate how many of those rooms in the total 175 takes the extra cleaning time:
one-fifth of the rooms takes 28 minutes to clean means that:
1 in every 5 rooms out of the 175 rooms take 28 minutes to clean
∴ Number of rooms with extra cleaning time = 1/5 of 175
= 1/5 × 175 = 0.2 × 175 = 35
∴ 35 rooms take 28 minutes each to be cleaned.
Now let us calculate the total cleaning time:
if 35 rooms take the extra cleaning time, then the number of rooms that have the normal cleaning time is as follows:
175 - 35 = 140
Total time:
140 rooms taking 20 minutes per room = 140 × 20 = 2,800 munites
35 rooms taking 28 minutes per room = 35 × 28 = 980 minutes
Total cleaning time = 2800 + 980 = 3780 minutes
converting to hours (1 hour = 60 minutes)
∴ 3780 minutes = 3780 ÷ 60 = 63 hours (2 days and 15 hours)
