Problem solving please help me guys...!

A mold press can produce 1200 buttons an hour.another mold press can produce 1500 buttons an hour.they need to produce 45,000 buttons.
A) how long will be needed if both presses are used to run the job?
B)if the press runs for 3 hours then the second press joins in, how long will it take for them to finish the run?

A) 1200 t +1500 t = 45000 where t is number of hours
2700 t = 45000
t = 45000/2700
=16 hr. 40 minutes....................Ans
B) 1200(t+3) +1500 t = 45000
1200 t + 3600 +1500t = 45000
2700t =45000 -3600=41400
t = 41400/2700
= 15 hr 20 minutes
Total time will be = 3hr +(15 hr 20 min)=18 hrs 20 min ...........Ans

working together they produce

2700 buttons in one hour

let x = number of hours

2700x = 45000
x = 16 2/3 hours
x = 16 hours and 40 minutes

if the first press runs for 3 hours, it produces
1200 * 3 = 3600 buttons

2700x = 45000 - 3600
2700x = 41400
x = 15 1/3 hours
x = 15 hours and 20 minutes