Luis Nunez begins walking at a rate of 8 mph. Forty-five minutes after he leaves, his wife, Kristin, realizes that Luis has forgotten his wallet. Kristin gets on her bicycle and begins riding at a rate of 28 mph along the same path that Luis took.
a) how long will it take Kristin to catch luis?
b) how far from their house will Kristin catch luis?

a). 18 minutes

b). 8.4 miles

Step-by-step explanation:

a). Let Luis meet Kristina after the time = h hours

So the distance traveled by Luis in h hours = Speed × time

= 8×h

= 8h miles

If Kristin started after 45 minutes of hours then the distance traveled by her

= Speed × time

= miles

Since after h hours distances traveled by Luis and Kristin are same so,

28h - 8h =

20h = 21

h = 1.05 hours

So the time taken by Kristin = (h - 0.75)

= 1.05 - 0.75

= 0.30 hours ≈ 18 minutes

b). Distance traveled by Luis before Kristin catches Luis = 8×1.05

= 8.4 miles

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)