Happy new year! Today’s SAT question of the day is a math question about stamps and envelopes.  How many more years before no one will know what those are??  Anyhow, the question is as follows:

A machine can insert letters in envelopes at the rate of 120 per minute. Another machine can stamp the envelopes at the rate of 3 per second. How many such stamping machines are needed to keep up with 18 inserting machines of this kind?

They’ve kindly underlined the first thing that we need to look at: we have a units mismatch.  One machine is in envelopes per minute, but the other is in envelopes per second. Let’s make them match: if the first machine can do 120 envelopes in 1 minute (or 60 seconds), it’s doing 2 envelopes per second.  So, how many stamping machines at a rate of 3 envelopes per second are needed to keep up with 18 of the 2 envelope per second inserting machines?

Note that the stamping machines are faster than the inserting machines, so we should need fewer than 18.  It’s always good to have a “reality check” like this so that you can feel confident in your answer!

Now let’s finish the math.  18 machines at a rate of 2 envelopes per second will insert letters into 36 envelopes per second (18 * 2).  36 envelopes divided by the stamping machine’s rate of 3 envelopes per second gives us 12 stamping machines.

Done!

Keep your machines and units straight and you will find this algebra/rate problem to be a breeze.