Question

Three people need to peel 1000 potatoes working together. Stacey starts at 2 PM peeling 20 potatoes per hour. Rob starts at 3 PM peeling 30 potatoes per hour, and James starts at 4 PM peeling 40 potatoes per hour. If they work continuously, at what time will the 1000 potatoes be peeled ?

Answer 1

2:20 am

Explanation:

Stacey's start time = 2 pm

Rate = 20 per hour

Rob start time = 3pm

Rate = 30 per hour

James start time = 4pm

Rate = 40 per hour

Number of potatoes = 1000

By 4 pm when James started :

(2 * 20) + (1 * 30) = 40 + 30 = 70

Potatoes left at 4pm = 1000 - 70 = 930 potatoes

Number of potatoes peeled per hour staring from 4 pm:

20 + 30 + 40 = 90 potatoes

Time taken to peel 930 potatoes will be :

930 / 90 = 10.333333 hours

(0.33333 * 60) = 19.9998 minutes

10.3333 hours = 10 hours 19.99998 minutes = 10 hours 20 minutes

Hence, from 4pm = 4pm + 10 hours 20 minutes = 2 : 20 a. M

Answer 2

They would be done by 2 : 18 AM

Explanation:

Key Information:

- Stacey starts at 2 PM peeling 20 potatoes per hour

- Rob starts at 3 PM peeling 30 potatoes per hour

- James starts at 4 PM peeling 40 potatoes per hour

At 5pm;

Stacy would have worked for 3 hours and would have peeled ( 3 * 20 = 60 potatoes)

Rob would have worked for 2 hours and would have peeled ( 2 * 30 = 60 potatoes)

James would have worked for an hour and would have peeled ( 1 * 40 = 40 potatoes)

Total number of potatoes peeled at 5pm = 60 + 60 + 40 = 160 potatoes

Potatoes left = 1000 - 160 = 840 potatoes.

The new peeling rate for three of them combined is (20 + 30+ 40 ) = 90 potatoes per hour.

Rate = potatoes left / time;

Time = Potatoes / Rate

Time = 840 / 90 = 9.3 hours = 9 hours 18 minutes

Total time taken = 9 hours 18 minutes + 3 hours = 12 hours 18 minutes

They would be done by 2 : 18 AM