Problema Solution
A sightseeing bus travels 40 miles to a scenic overlook. The rate returning is twice the rate going, and the travel time or the round trip is 2 hours. Find the rate for the return part o the trip.
Answer provided by our tutors
let
d = 40 mi the distance in one direction
v = the rate of going, v>0
2v = the rate returning (the rate returning is twice the rate going)
t1 = the time of the going trip
t2 = the time of the returning trip
v = d/t1
since distance = rate*time we have
v*t1 = 2v*t2 divide both sides by v
t1 = 2t2
we also know the total time of the trip is 2 hours:
t1 + t2 = 2
by solving the system of equations:
t1 = 2t2
t1 + t2 = 2
we find
t1 = 4/3 hr
t2 = 2/3 hr
click here to see the step by step solution of the system of equations:
v = d/t1
v = 40/(4/3)
v = 30 mph
2v = 2*30 = 60 mph
the rate of the return trip is 60 mph.