Math Problem of the Week - Algebra and Up - Aug. 21, 2022 to Aug. 27, 2022

Algebra and Up:

Question: It takes Alice 45 minutes to complete a jigsaw puzzle. It takes Keisha an hour to complete a jigsaw puzzle of the same size. If they work together on the same jigsaw puzzle, how long will it take them to complete it?

Answer: 25 5/7 minutes

Solution: Alice's puzzle completing rate is 1 puzzle over 45 minutes, or 1/45. Keish's rate is 1/60. If we add them together, we 1t, the rate at which they can solve 1 puzzle together.

1/45 + 1/60 = 1/t

To solve this, we need to multiply each side by the LCM of the denomi¬nators, which is 180t. The result is: 4t + 3t = 180 t = 255/7