Last one, bikes on a trail distance variable

Question

Sean and Madison bike along the same trail. Madison bike the entire trail at a speed of 20 MPH and Sean bikes it at a speed of 15 MPH. Madison finishes biking the entire trail 8 minutes before Sean.

 

How many miles long is the bike trail?

Answer 1

distance=rate*time

d=r*t

d=(15)(t) for Sean

d=(20)(t-8/60) for Madison   (8 minutes is 8/60 of an hour)

set the two right sides equal to each other because they both equal d

(15)(t)=(20)(t-2/15)

15t=20t-40/15

20t-15t=40/15

5t=40/15

multiply both sides by 1/5

t=(1/5)(40/15)

t=8/15 of an hour

d=(15)(t)

d=(15)(8/15)

d=8 miles long is the bike trail