SOLUTION: Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles

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Question 262931: Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?
A. 2 hours
B. 4 ½ hours
C. 5 ¾ hours
D. 6 hours
E. 7 ½ hours

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I have a stopwatch and I'll start it when the 2nd
cyclist leaves. At that time the 1st cyclist has gone
r%5B1%5D%2A3
6%2A3+=+18 mi
Now they will each go for the same time on my stopwatch, so
t%5B1%5D+=+t%5B2%5D, which I'll just call t
d%5B1%5D+=+r%5B1%5D%2At
d%5B2%5D+=+r%5B2%5D%2At
From these,
d%5B1%5D%2Fr%5B1%5D+=+d%5B2%5D%2Fr%5B2%5D
d%5B1%5D%2Ar%5B2%5D+=+d%5B2%5D%2Ar%5B1%5D
10d%5B1%5D+=+6d%5B2%5D
d%5B1%5D+=+.6d%5B2%5D
I know 1 more thing about the distances:
d%5B2%5D+=+d%5B1%5D+%2B+18, since the 2nd cyclist has to make up
the headstart the 1st one got
Substituting:
d%5B2%5D+=+.6d%5B2%5D+%2B+18
.4d%5B2%5D+=+18
d%5B2%5D+=+45 mi
and
d%5B1%5D+=+.6%2Ad%5B2%5D
d%5B1%5D+=+.6%2A45
d%5B1%5D+=+27 mi
Now, I need to find t
(1) d%5B1%5D+=+r%5B1%5D%2At
(2) d%5B2%5D+=+r%5B2%5D%2At
-------------------
(1) 27+=+6t
t+=+4.5 hrs
and, also
(2) 45+=+10t
t+=+4.5 hrs
How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?
This means that the 3 hr headstart is not to be included in answer
so, 4.5 hrs will pass
The answer is B