A jet plane traveling at a rate of 550 mph overtakes another

A jet plane traveling at a rate of 550 mph overtakes another plane that had a 3 hour head start and is traveling at a rate of 250 mph. How far from the starting point does the jet overtake the other plane?

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
let t=time required for second plane to catch the first
Distance first plane travels=3*250+250t (remember, three hour head start)
Distance 2nd plane travels=550t
Now when the above two distances are equal, the second plane will have overtaken the first, so:
3*250+250t=550t or
750+250t=550t subtract 250t from each side
750+250t-250t=550-250t collect like terms
300t=750 divide each side by 300
t=2.5 hours---------------time required for 2nd plane to overtake first
distance first plane travels=750+250*2.5=1375 mi
distance 2nd plane travels=550*2.5=1375 mi