Question

Bob left home, riding his bike at a rate of 10mph to go to the lake. Cheryl, his wife, left 45 minutes ( 0.75 hours) later, driving her car at a rate of 25mph. How long will it take Cheryl to catch up to Bob?

Answer 1

It takes Cheryl 0.5 hour (or 30 minutes) to catch Bob.

Explanation:

Bob:

rate = 10 mph

time = t

distance
`=10t` miles

Cheryl:

rate = 25 mph

time = t - 0.75 hours

distance
`=25(t-0.75)` miles

If Cheryl catchs up to Bob, then their distances are the same:

`10t=25(t-0.75)\\ \\10t=25t-18.75\\ \\10t-25t=-18.75\\ \\-15t=-18.75\\ \\15t=18.75\\ \\t=1.25`

It takes Cheryl 1.25 - 0.75 = 0.5 hour (or 30 minutes) to catch Bob.