Question

Shelby leaves her house at 9 a.m. on her bike at a speed of 320 meters per minute. At 10:30 a.m. her brother, Colby, leaves the house on his bike and tries to catch up with Shelby. Colby rides at a speed of 500 meters per minute. At what time will Colby catch up with Shelby?

Answer 1

Let the time from 9:00 am until Colby catches her be t minutes
distance covered by Shelby in that time = 320t metres
distance covered by Colby in that time = 500(t - 90)
but they went the same distance, so
500(t-90) = 320t
......
t = 250 minutes or 4 hours and 10 minutes
So he catches up to her at 1:10 pm

check: Shelby went at 320 metres/minute for 250 minutes = 80,000 metres
Colby went for 160 minutes (13:10 - 10:30) at 500 m/min = 80,000 metres