A red light flashes every 2 minutes and a blue light flashes every 3.5 minutes. Suppose both lights flash together at noon. What is the first time after 1 p.m. that both lights will flash together?

Answer 1

After 1:00, when they last flashed together:
When they first coincide again, let the red light have flashed x time
When they first coincide again, let the blue light have flashed y time

then 2x = 3.5y
4x = 7y
smallest value: x = 7 and y = 4
time = 4x = 28 minutes , so they will coincide at 1:28 pm

check:
red will flash at: 1:00, 1:02, ... 1:26, 1:28, 1:30, ...
blue will flash at 1:00, 1:03.5, 1:07, 1:10.5, 1:14, 1:17.5, 1:21, 1:24.5, 1:28, 1:31.5 ...