Dori and Malory are tracking their steps taken as a health goal. Dori leaves her house at 12:00 p. m. and walks at 50 steps per minute. Malory leaves her house at 12:20 p. m. and walks at 90 steps per minute. At what time will Malory's steps catch up to Dori's steps?

Let n = minutes since 12:00 pm when Malory catches up to Dori.

Dori travels

(50 steps/min) * (n minutes) = 50n steps

Malory begins walking at 12:20 pm, so she walks for (n - 20) minutes. She travels

(90 steps/min) * (n - 20 min) = 90n - 1800 steps

Equate the steps traveled by Dori and Malory.

90n - 1800 = 50n

40n = 1800

n = 45 min

The time corresponding to n = 45 min is 12:45 pm

Answer: 12:45 pm