SOLUTION: Jones can run around a 400-meter track in 65 seconds. How long does Smith take to run the 400 meters if he meets Jones in 35 seconds after they start together in a race around the

Question 160640: Jones can run around a 400-meter track in 65 seconds. How long does Smith take to run the 400 meters if he meets Jones in 35 seconds after they start together in a race around the track in opposite directions?
Not sure how to set up the equation for this problem.
Found 2 solutions by checkley77, ankor@dixie-net.com:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
400/65+400/35=6.15+11.43=17.58 COMBINED RATE OF BOTH RUNNERS.
400/17.58=T
T=22.75 SEC. IS THE TIME THEY WILL MEET.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Jones can run around a 400-meter track in 65 seconds. How long does Smith take
to run the 400 meters if he meets Jones in 35 seconds after they start together
in a race around the track in opposite directions?
:
When they meet, they will have traveled a total of 400 meters in 35 seconds
:
Find Jone's speed in meters/sec: = 6.154 m/sec
:
Let s = Smith's speed in m/sec
:
Write a dist equation; Dist = time * speed
:
35s + 35(6.154) = 400
:
35s + 215.39 = 400
:
35s = 400 - 215.39
:
35s = 184.61
s =
s = 5.275 m/sec is Smith's speed
:
Find time for Smith to run 400 m:
= 75.83 sec to run 400 m
:
:
Check solution:
35 * 5.275 = 184.625 m
35 * 6.154 = 215.39
------------------
Total dist = 400.0
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