select the correct answer from the drop - down menu. phoebe runs a t - shirt printing business. she ships…

select the correct answer from the drop - down menu. phoebe runs a t - shirt printing business. she ships the t - shirts to retailers in boxes of 200. she has two automated printing machines that can print designs on t - shirts. one machine can print 200 t - shirts in 50 minutes. the other machine can print 200 t - shirts in 150 minutes. if the two machines work at the same time, they can print 200 t - shirts in minutes. reset next 36.5 37.5 38.5

select the correct answer from the drop - down menu. phoebe runs a t - shirt printing business. she ships the t - shirts to retailers in boxes of 200. she has two automated printing machines that can print designs on t - shirts. one machine can print 200 t - shirts in 50 minutes. the other machine can print 200 t - shirts in 150 minutes. if the two machines work at the same time, they can print 200 t - shirts in minutes. reset next 36.5 37.5 38.5

Answer

Explanation:

Step1: Calculate the rate of each machine

The first machine can print 200 T - shirts in 50 minutes, so its rate $r_1=\frac{200}{50} = 4$ T - shirts per minute. The second machine can print 200 T - shirts in 150 minutes, so its rate $r_2=\frac{200}{150}=\frac{4}{3}$ T - shirts per minute.

Step2: Calculate the combined rate

The combined rate $r = r_1 + r_2=4+\frac{4}{3}=\frac{12 + 4}{3}=\frac{16}{3}$ T - shirts per minute.

Step3: Calculate the time to print 200 T - shirts together

Let $t$ be the time. We know that the work $W = 200$ and $W=rt$. So $t=\frac{W}{r}=\frac{200}{\frac{16}{3}}=200\times\frac{3}{16}=37.5$ minutes.

Answer:

37.5