Zip and Mimi biking

Question

Zip left the house at noon and rode their bike at a speed of 6.7 mph. 10 minutes later Mimi left the same house at a speed of 14 mph. At a certain point in time, Mimi caught up with zip and so they both stopped biking.

how much total time did zip bike?

Answer 1

After 10 minutes (1/6 of an hour), Zip had ridden (6.7 m/hr)(1/6 hr) = 1.1167 miles.

Let "x" be the distance that Zip rode after that time until the time that Mimi caught up. The time that Zip rode then (during that 2nd portion of the ride) is (x/6.7) hrs. The time that Mimi rode is (x + 1.1167)/14 hrs. These two times are the same so:

x/6.7 = (x + 1.1167)/14

Cross multiplying, we get:

14x = 6.7(x + 1.1167)

14x = 6.7x + 7.4817

7.3x = 7.4817

x = 7.4817/7.3 = 1.025 miles

Since the time Zip rode for the second portion of the ride was x/6.7, they rode 0.153 hrs (multiplying this by 60 gives 9.18 minutes). So the total time Zip rode was 9.18 + 10 = 19.18 minutes