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?
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
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
To determine how long it will take Erik to pass Stefan, we need to find the time it takes for their distances to be equal.
Let's assume t is the time it takes for Erik to pass Stefan.
Since Stefan is cycling for t time and his average speed is 10 mph, his distance covered would be 10t miles.
Now, since Erik starts cycling 30 minutes (0.5 hours) later, his cycling time is t - 0.5, and his average speed is 16 mph. Therefore, his distance covered would be 16(t - 0.5) miles.
Now, for the time when Erik passes Stefan, their distances will be equal. So, we can set up an equation:
10t = 16(t - 0.5)
Let's solve for t:
10t = 16t - 8
8 = 6t
t = 1.33 hours (or approximately 1 hour and 20 minutes)
Therefore, it will take Erik approximately 1 hour and 20 minutes to pass Stefan.