Mercedes starts jogging at 5 miles per hour. One-half hour later, Karen starts jogging on the same route at 7 miles per hour. How long will it take Karen to catch Mercedes?

Question

I did: 7(t-1/2) = 5t which equals 1 3/4 hours which is apparently wrong.

I've seen two types of methods for these type of questions and they both give a different answer.

The correct answer is apparently: 5(t+1/2) = 7t which equals 1 1/4 hours.

Take another question like this: A bus leaves a station at 8:00 a.m. and averages 30 mi/h. Another bus leaves the same station following the same route two hours after the first and averages 50 mi/h. When will the second bus catch up to the first?

They used my method for this one which was 30t = 50(t-2) which equals 3 hours.

Now if i use the other method 30(t+2) = 50t i get 5 hours.

Which one is correct and why?

Answer 1

t represents the time Mercedes is jogging

t - 0.5 represents the time Karen is jogging

5t = 7(t - 0.5)

5t = 7t - 3.5

-2t = -3.5

t = 1.75

t - 0.5 = 1.25