Solution to Riddle of the Week: The Chess Practice Problem

Laura Feiveson

From Popular Mechanics

This is a solution to This Riddle Is Like an Especially Cruel SAT Problem. Can You Find the Answer?, part of our Riddle of the Week series.

This Riddle Is Like an Especially Cruel SAT Problem. Can You Find the Answer?

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Let’s call the spot at which Amanda and Matt meet on the road, point M. In this problem, Amanda drives from their home to point M, where she picks up Matt, and then drives back to their home. Let’s call the time it takes her to do this “T”.

Photo credit: Laura Feiveson

We don’t know T, but we do know the time it took Amanda to do this is 40 minutes less than the time it usually takes her to drive back and forth from school.

Photo credit: Laura Feiveson

From this, we can infer the back-and-forth trip she did not drive (from M to school and back to M) must take 40 minutes. Since she drives at a constant speed, the one-way trip from M to school must therefore take 20 minutes.

Photo credit: Laura Feiveson

Since we know Amanda times her day to arrive at school for pickup at exactly 5 p.m., she must have reached M at 20 minutes before pickup, or at 4:40 pm.

Now, we know from the problem that Matt left chess club one hour before he met Amanda at point M. Thus, he must have left at 3:40 pm. Since chess typically ends at 5 pm, we have our answer: Matt missed 1 hour and 20 minutes of chess practice.

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