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How to compute smth like this quickly?
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Swagatalaxmi
I­n a certain factory, five different machines-Machines A through E-produce ceramic figurines, each at different rates. The machines were all brought online at different times, each continuously producing figurines at its own constant rate until 8:00 p.m.:

• Machine A at 1:00 p.m., producing 1,000 figurines per hour
• Machine B at 1:15 p.m., producing 500 figurines per hour
• Machine C at 1:45 p.m., producing 1,500 figurines per hour
• Machine D at 2:00 p.m., producing 400 figurines per hour
• Machine E at 2:45 p.m., producing 900 figurines per hour

At 2:45, when Machine E was brought online, the other four machines had produced a total of x figurines. After 2:45, the total combined rate of production for all five machines was y figurines per hour.

Select a value for x and a value for y so that the above statement accurately reflects the given information. Make only two selections, one in each column.


Value of x:

Let's approximate: From 1:45 till 2:45, the 4 machines (except E) are working

So they would have produced more than 1000 + 500 + 1500 + 400 = 3400 figurines.
Machine B works for 30 mins extra while machine D works for 15 mins less so they kind of cancel each other off (diff of a 100 or 200 so ignore since options are far off)
Machine A works 45 mins more so another 750 figurines were made.

Hence total number of figurines by 2:45 would be 4300, the only possible option.

Value of y:

The total combined rate of production for all five machines after 2:45 was simply the sum of their individual rates (since rates are additive)
So y = 3400 + 900 = 4300
(We had calculated 3400 in the step above)

Here is a video on work rate concepts: https://youtu.be/88NFTttkJmA

Select 4300 for both
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