Math for 6th grade

Question

Carl goes running every 3 days. He does push-ups every 4 days. Every 6 days, he swims. What is the first day he will do all three When is the second day he will do all three When is the third day he will do all three

Answer 1

Let R, P and S refer to Running, Push-ups and Swimming.

R happens on days 2, 6, 9, 12, 15, 18, 21, 24, 27, etc

P happens on days 4, 8, 12, 16, 20, 24, 28, etc.

S happens on days 6, 12, 18, 24, 30, etc

Looking at the chart, the common days are 12 and 24.

As it happens, 12 is the first number for which 3, 4 and 6 are factors. Every multiple of 12, e.g. 24 = 2x12, has this trait.

The answer to the question is day 12