math question

Question

Three cars left Town A for Town B. Car B began its journey 45 minutes after Car A. Car C began its journey 15 minutes after Car B. Car C caught up with Car A 25 minutes later. It then caught up with Car B another 15 minutes later. When did Car B catch up with Car A?

Answer 1

12 hours after C left

or 11 hours and 45 minutes after C caught up to B that C catches up to A

Let A, B, C = the speeds of each car

C=2B 30/15 = C/B, multiply by 8

8C=16B

8C=17A 85/45 = C/A

subtract 8C=17B from 8C=16A

to get 16A -17B=0

16B=17A

B/A =17/16

let x = the time car C drives to catch up to A

(45+x)/x = 17/16

16(45+x) =17x

720-16x =17x

x =720 minutes = 12 hours= total driving time for car C to catch car A

12 - 45 min = 11 hours and 15 minutes to catch up to A after catching B