Problema Solution
a bus leaves a station at 8:00 and averages 30 mi/h another bus leaves the same station following the same route two hours after the first and averages 50 mi/h when will the second bus catch up with the first one
Answer provided by our tutors
let
v1 = 30 mi/h the speed of the first bus
t1 = the time of the travel of the first bus (before the catching up)
v2 = 50 mi/h
t2 = the time of the travel of the second bus (before the catching up)
since the second bus leaves the station 2 hours after the first we have
t1 = t2 + 2
the formula for the speed is speed = distance/time => distance=speed*time
v1*t1 = v2*t2
30*t1 = 50*t2
by solving the system of equations
t1 = t2 + 2
30*t1 = 50*t2
we find
t1 = 5 h
t2 = 3 h
click here to see the step by step solution of the system of equations
5 hours after 8:00 is 13:00 hours.
the second bus will catch up with the first at 13:00 hours.