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?

[spoiler]ans = 6[/spoiler]

Ex-chef = 8 hours.
Novice=12 hours.
let work = 24
rate of ex-chef=3,rate of novice=2
total rate=5
work=24
time taken by 1 ex and 1 novice = 24/5 = 288 minutes
time taken by x ex and x novice workers = 288/x = (60+36) = 96
x=288/96 = 3
Thus total chefs=3*2=6

Hi,
Let 'T' be the taken for n exp. chefs and n novice chefs to finish the work.
1/T = n(1/t1 + 1/t2). Given that T = 1hour 36 mins = 1|+3/5 = 8/5 hours
So, 1/(8/5) = n(1/8 + 1/12) =>5/8 = n(5/24) =>n=3.
So, total number of chefs required is n+n = 6.