SOLUTION: John can run a certain course in 9 min and Henry can run it in 6 min. If they start at opposite ends and run towards one another, how long will they run before they meet?

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Question 5376: John can run a certain course in 9 min and Henry can run it in 6 min. If they start at opposite ends and run towards one another, how long will they run before they meet?
Answer by Abbey(339) About Me  (Show Source):
You can put this solution on YOUR website!
Set this up by determining how much distance each covers in one minute:
John runs 1%2F9 of the distance each minute
Henry runs 1%2F6 of the distance each minute
When running from opposite ends they are covering a distance of John + Henry, or
1%2F9%2B1%2F6 = 2%2F18%2B3%2F18=5%2F18
After the first minute they are 5%2F18 of the distance
After the second minute they are 10%2F18 of the distance... and so on
Set this up as a proportionality %28Rate%29%2F%28total+distance%29+=+%281+minute%29%2F%28total+time%29:
%285%2F18%29=1%2Fx
Cross multiply:
5x=18
Divide both sides by 5
x=18%2F5+=+3.6
So it took them 3.6 minutes to meet.