SOLUTION: Rick robbed a bank and left town at 64 mph. His crime was discovered 45 minutes later when the sheriff took off in hot pursuit at 80 mph. How long until the sheriff catches up?

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Question 220538: Rick robbed a bank and left town at 64 mph. His crime was discovered 45 minutes later when the sheriff took off in hot pursuit at 80 mph. How long until the sheriff catches up?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Assume I have a stopwatch. I will start the stopwatch
when the sheriff leaves. At that time, Rick has travelled
d%5Br%5D+=+64%2A%283%2F4%29 (45 min is 3/4 of an hour)
d%5Br%5D+=+48 mi
So, Rick has a 48 mi headstart
From this headstart to where the sheriff catches him,
call d in miles
For the sheriff:
d+%2B+48+=+80%2At
For Rick:
d+=+64%2At
By substitution:
64t+%2B+48+=+80t
16t+=+48
t+=+3hrs
The sheriff catches him 3 hrs after the sheriff leaves town
check answer:
d+=+64t (for Rick)
d+=+64%2A3
d+=+192 mi
So, Rick went a total of 48+%2B+192+=+240 mi at 64 mi/hr
The sheriff went 240 mi also at 80 mi/hr
For Rick:
240+=+64%2At%5Br%5D
t%5Br%5D+=+3.75 hrs for the whole trip for Rick
For Sheriff:
240+=+80%2At%5Bs%5D
t%5Bs%5D+=+3 hrs for the whole trip for Sheriff
Note that 3.75+-+3+=+.75, which is
the 45 min headstart that Rick had