Stefan is bicycling on a bike trail at an average of 10 mph. Erik starts bicycling on the same trail 30 minutes later at 16 mph. How long will it take Erik to pass Stefan?

Answer 1

When Eric passes Stefan, they both will have gone the same distance
since d = rate x time
10t = 30(t - 1/2)
10t= 30t - 15
t = 3/4 hr or 45 minutes

but Eric only traveled for t-1/2 hours = 45-30 minutes or 15 minutes

check:
Stefan went 3/4 hrs at 10 mph = 30/4 miles
Eric went 1/4 hrs at 30 mph = 30/h miles

my answer is correct

Answer 2

Stefan has a 5 mi head start ... 10 mph * 30 min

Erik catches up at the rate of 6 mph ... 16 mph - 10 mph

time to catch up (pass) ... 5 mi / 6 mph