Question

A particular stretch of trail is two miles long. Angela bikes at a rate of 20 mph. Brad jogs at a rate of 5 mph. At 8:00 AM one morning, Brad starts out at the south end of the trail and begins jogging north. A quarter of an hour later (in other words, 8:15 AM), Angela also starts at the south end and begins heading north as well. Does Angela pass Brad before he gets to the north end? If she does, at what time does she pass him, and what distance have they each traveled? (in other words, how far are both of them from the south end)

Answer 1

time taken by Brad,

t1 = distance / speed

= 2 mi / 5 mph

= 0.4 h

= 0.4*60 min

= 24 min

time taken by Angela,

t2 = distance / speed

= 2 mi / 20 mph

= 0.1 h

= 0.1*60 min

= 6 min

Even if Angela starts 15 mins late, she will reach North at 8.21 while Brad does at 8.24

So, Angela pass Brad

Lets say Angela pass Brad at t minutes after 8.00 Am

distance moves should be same for both

distance moves by Angela = distance moves by Brad

20*(t-15) = 5*t

20t - 300 = 5t

15t = 300

t = 20

So, she passed at 8.20