SOLUTION: A runner starts at the beginning of a runners’ path and runs at a constant rate of 5 mi/hr. Six minutes later a second runner begins at the same point running at a rate of 7

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Question 399516: A runner starts at the beginning of a runners’ path and runs at a
constant rate of 5 mi/hr. Six minutes later a second runner begins at the
same point running at a rate of 7 mi/hr and following the same course.
How long will it take the second runner to reach the first?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In 6 min, the 1st runner goes 5%2A%281%2F10%29+=+.5 mi
(note that 6 min = 6/60 hr)
Now the 2 runners will run for the same amount of time
with a half-mile headstart for runner #1.
2nd runner:
(1) d+=+7t
1st runner:
(2) d+-+.5+=+5t
Substitute (1) in (2):
(2) 7t+-+.5+=+5t
2t+=+.5
t+=+.25 hr
It will take the 2nd runner 15 min to catch the 1st
check answer:
d+=+7%2A%281%2F4%29
d+=+1.75
and, also,
d+-+.5+=+5%2A%281%2F4%29
d+=+.5+%2B+1.25
d+=+1.75
OK