This should be really simple but I'm getting stuck and I'm probably extremely dumb..

I know that a machine receives two kind of parts:

Type 1 -> with frequency 50 per week, each one is processed for 20 minutes
Type 2 -> with frequency 100 per week, each one is processed for 8 minutes

It was told me to consider (in working hours) 1 week = 2400 minutes.

I have to calculate the average arrival rate of the machine and the average service time of the machine.

Average arrival rate of the machine = 50 pieces per week + 100 pieces per week = 150 pieces per week, this is simple since each piece counts as an arrival (they're all equal)

I'm confused with the Average service time per piece of the machine...

I tried: 

the machine can serve 2400/20 type 1 pieces per week = 120
and 2400 / 8 type 2 pieces per week = 300

so average\_service\_rate = (120\*50 + 300\*100) / 150 = 240, but this is wrong according to my solution (which is 200)... 

if I use service times it works:
time per each type 1 piece: 20 min
time per each type 2 piece: 8 min
average\_time\_per\_piece = (20\*50 + 8\*100)/150 = 12 min, i.e. 12/2400 week
so 1/averaget\_time\_per\_piece = average\_service\_rate = 2400/12 = 200. And this is the right value.

My question is: why my first approach with the average frequency didn't work? What's wrong with it?