Question

Roger can run one mile in 14 minutes. jeff can run one mile in 12 minutes. if jeff gives roger a 1 minute head​ start, how long will it take before jeff catches up to​ roger? how far will each have​ run?

Answer 1

Let the time taken by Roger = x minutes
Speed of Roger = (1/12)
Distance covered by Roger =(x)/12 ------(1)

Time taken by Jeff = x+1 minutes
Speed of Jeff = (1/14)
Distance covered by Jeff =(x+1)/14 ------(2)

Distance covered by Jeff = Distance covered by Roger

(x+1)/14 = x/12
12x +12 = 14x
2x = 12
x=6
Substitute the value of x in equation (1),
Distance covered = x/12 = 6/12 = 1/2
Time taken by Jeff to catch up to Roger is 7 minutes
Distance covered by them = 1/2 mile