Question

Two machines are printing shirts. The first machine can produce 2,100 shirts in 140 minutes. The second machine can produce 2,400 shirts in 120 minutes. If the two machines work together, how long will it take them to produce 7,350 shirts? If necessary, round your answer to the nearest whole number._(blank)_ minutesType your whole number answer (without units) below.

Answer 1

The first machine can produce 2,100 shirts in 140 min, then the shirts per minute it can produce is:

`\frac{2100\text{ shirts}}{140\text{ min}}=15\text{ shirts per minute}`

The second machine can produce 2,400 shirts in 120 min, then it can produce in one minute:

`\frac{2400\text{ shirts}}{120\text{ min}}=20\text{ shirts per minute}`

If the two machines work together, they can produce 15+20=35 shirts per minute, then to produce 7,350 shirts it will take:

`\begin{gathered} \frac{35\text{ shirts}}{1\min }=\frac{7350\text{ shirts}}{x} \\ x=\frac{7350\text{ shirts}\cdot1\min }{35\text{ shirts}} \\ x=210\text{ min} \end{gathered}`

The answer is 210 minutes.