#### jonah2.0

##### Full Member

- Joined
- Apr 29, 2014

- Messages
- 387

**Beer soaked ramblings and correction follows.**Let's put it in a real figure.Let ...

Let the distance from Lake Geneva to Chicago be 83 miles.

At 5 minutes, the Speedy Coach bus that left 5 min. earlier that Travis must first pass has a headstart of (5/60)*83/(90/60) or 4 11/18 miles. Since Leisure Tour buses take 60 minutes to reach Chicago, it follows that its speed or rate is 83/(60/60) or 83 mph. The first Speedy Coach bus that Travis passes is at the point when (5 min. headstart) + 83/(90/60)*x = 83*x where x is the time when Travis is side by side with the bus with the 5 min. headstart. This is the time when both buses have covered the same distance which is 13 5/6 miles.

The 2nd Speedy Coach bus that Travis must pass has a head start of (5 + 10) min. or 13 5/6 miles. They will be side by side at the point when (5 + 10) min headstart + 83/(90/60)*x = 83*x. This is the time when both buses have covered the same distance which is 41.5 miles (halfway through Chicago).

The 3rd Speedy Coach bus that Travis must pass has a head start of (5 + 10*2) min. or 23 1/18 miles. They will be side by side at the point when (5 + 10*2) min. headstart + 83/(90/60)*x = 83*x. This is the time when both buses have covered the same distance which is 69 1/6 miles (5/6 of the way through Chicago).

Travis cannot pass the 4th bus which has a headstart of (5 + 10*4) min. or 32 5/18 miles since it can cover the remaining 50 13/18 miles (83 - 32 5/18) in 33 22/27 minutes [(50 13/18)/(90/60)] while Travis is still at the 46 1259/1620 miles point in 33 22/27 minutes.