Problem Solving

On a wedding catering service, An experienced chef can prepare a service for a wedding in 8 hours while an novice chef would finish the preparations in 12 hours.

If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?
Explain this question

(1)2
(2)3
(3)4
(4)6
(5)8

mundasingh123 wrote:On a wedding catering service, An experienced chef can prepare a service for a wedding in 8 hours while an novice chef would finish the preparations in 12 hours.

If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?
Explain this question

(1)2
(2)3
(3)4
(4)6
(5)8

Let service = 24 units.
Rate for each experienced chef = w/t = 24/8 = 3 units per hour.
Rate for each novice chef = w/t = 24/12 = 2 units per hour.
Combined rate for 1 experienced chef and 1 novice chef working together = 3+2 = 5 units per hour.
To produce 24 units in 1.6 hours, rate = w/t = 24/1.6 = 15 units per hour.
Since each pair of chefs produces 5 units per hour, number of pairs needed = 15/5 = 3.
Total number of chefs in 3 pairs = 2*3 = 6.

The correct answer is D.

work done by exp chef in 1 hr 1/8
work done by novice chef in 1 hr is 1/12
combined rate 1/8 + 1/12 = 5/24
now let n exp chef and n novice chef work together

combined work done in 1 hr is n/8 + n/12 = 5n/24
thus work done combined in 1.6 hrs(1 hr and 36 min) is 5n/24 *1.6 , which is equal to 1 job
therefore n= 3
total no of chefs is 2n = 6

1+ for D) 6