Question 214967
Two cyclists start biking from a trail 3 hours apart. The 2nd cyclist traveled at 10 miles per hour and starts 3 hours after the 1st cyclist who is traveling at 6 miles per hour. How much time will pass before the 2nd cyclist catches up with the 1st cyclist from the time the 2nd cyclist started? 


Step 1.  Let x be the time 2nd cyclist catches up with the 1st cyclist.


Step 2.  Let 6x+18  total distance traveled by first cyclist and where 3 hours * 6 mph =18 miles travels after three hours plus 6x miles.


Step 3.  Let 10x distance traveled by 2nd cyclist.


Step 4.  Set expression in Steps 2 and 3 to be equal since they will have traveled the same distance.


{{{6x+18=10x}}}


{{{4x=18}}}


{{{x=4.5 hours}}}


Step 5.  It will take 4.5 hours to for the second cyclist to catch up with the first cyclist.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J