Answer: it will take Sebastian's mom 45 minutes to catch up with the bus.
Step-by-step explanation:
By the time Sebastian's mom catches up with the bus, she would have covered the same distance with the bus.
Let t represent the time it will take for Sebastian's mom to catch up with the bus.
Distance = speed × time
Sebastian's school bus averages 28 miles per hour.
Distance covered by Sebastian's school bus in t hours is
28 × t = 28t
Sebastian's mom travelled at an average speed of 42mph. Since she left home 0.25 hour after Sebastian, the time it would take her to cover the same distance is
(t - 0.25) hour. Distance covered in
(t - 0.25) hour is
42(t - 0.25)
Since the distance covered is the same, then
28t = 42(t - 0.25)
28t = 42t - 10.5
42t - 28t = 10.5
14t = 10.5
t = 10.5/14
t = 0.75
Converting to minutes, it becomes
0.75 × 60 = 45 minutes
