Problem 6.
How fast to drive to the cemetery

My little brother left two minutes ago on his bike to ride with his friends to the cemetery. If he pedals at 5 miles an hour to the cemetery, which is 1 mile from here, and I go the back way (2 and a half miles) so he won't see the car, how fast do I have to drive Dad's car to get there at least a full minute ahead of him so I can hide and scare them?

Answer: 17 miles per hour

1a) Little brothers travel time:
1 mile / 5 mph = 1/5 hour
1/5 hour * 60 minutes per hour = 12 minutes

1b) Little brothers time to cemetery
12 minutes total less 2 minutes head start = 10 minutes

2a) Older child’s time to cemetery
10 minutes - 1 minute to hide = 9 minutes

2b) Older child’s distance = 2.5 miles (given in the problem)

2c) Older child’s required speed
2.5 miles per 9 minutes = 2.5 miles divided by 9 minutes times 60 minutes per hour
(2.5 * 60) / (9 * 1 ) = 16.66667

Neglecting time to park, etc.