An assembly line produces 2 toasters per minute. It is 2:00pm and the line has finished 560 out of its goal of 900 for the day. The line stops at 5:00pm. A co-worker is urging you to stop the line for a half hour break, saying that you will make the goal anyway. Should you stop the line for a half hour break?

I won't stop the line for a half hour break.

Step-by-step explanation:

Proportions

One quantity A is said to be proportional to other B if A can always be obtained by multiplying or dividing B by any constant number. Numbers {4,8,12} are proportional to {2,4,6} because they can be computed as twice their value

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There is a situation described in the problem where we need to know if there will be enough time to produce the 900 toasters (the goal for the day) when the assembly line is stopped by half an hour.

Actual time: 2:00 pm

Final time: 5:00 pm

Rate of production: 2 toasters/minute

Actual production: 560 toasters

Updated goal: 900-560 = 340 toasters

Those 340 toasters must be produced in the remaining 3 hours (180 minutes) of work. If the assembly line stops for half an hour (30 minutes), there will be only 150 minutes to finish the goal production. At a rate of 2 toasters/minute, there will be 2*150 = 300 toasters produced. But we need to produce 340 more toasters, so that break cannot be granted or we'll be 40 toasters under goal.

It the line keeps producing for 180 minutes, it would produce 2*180 = 360 toasters, 20 more than the goal.

Note: The maximum break time that can be granted is 20/2 = 10 minutes