SOLUTION: A long distance runner started on a course running at an average speed of 6 mph. One hour later, a second runner began the same course at an average speed of 8 mph. How long after

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Question 1127482: A long distance runner started on a course running at an average speed of 6 mph. One hour later, a second runner began the same course at an average speed of 8 mph. How long after the second runner started will the second runner overtake the first runner?
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A long distance runner started on a course running at an average speed of 6 mph. One hour later, a second runner began the same course at an average speed of 8 mph.
How long after the second runner started will the second runner overtake the first runner?
:
let t = 2nd runner's time when overtaking the 1st runner
then
(t+1) = 1st runner's time
:
When the 2nd runner catches the 1st, they will have traveled the same distance.
write a distance equation; speed * time
8t = 6(t+1)
8t = 6t + 6
8t - 6t = 6
2t = 6
t = 6/2
t = 3 hrs for the 2nd runner to catch the 1st.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
1st runner's head start in miles:
+d%5B1%5D+=+6%2A1+
+d%5B1%5D+=+6+
-------------------
Let +d+ = distance 2nd runner travels until
overtaking the 1st runner
Let +t+ = time in hrs for 2nd runner to
overtake the 1st runner
-------------------------------------------------
Equation for 1st runner:
(1) +d+-+d%5B1%5D+=+6%2At+
Equation for 2nd runner:
(2) +d+=+8t+
----------------------------
Plug (2) into (1)
(1) +d+-+6+=+6t+
(1) +8t+-+6+=+6t+
(1) +2t+=+6+
(1) +t+=+3+
----------------------
In 3 hrs the 2nd runner overtakes the first
----------------------
check:
(2) +d+=+8%2A3+
(2) +d+=+24+ mi
(1) +24+-+6+=+6%2A3+
(1) +18+=+18+
OK