Problema Solution
a professor drove from denver to boulder during rush hour at an average speed of 30 miles per hour, and then drove back the same way at an average speed of 45 miles per hour. if the round trip took 1 hour and 45 minutes, how many miles is the professors one way trip from denver to boulder?
Answer provided by our tutors
let
v1 = 30 mph from denver to boulder
t1 = time of the trip from denver to boulder
v2 = 45 mph from boulder to denver
t2 = time of the trip from boulder to denver
t1 + t2 = 1 hour 45 min = 1 45/60 = 1.75 hours
d = the distance from denver to boulder
since the speed v = d/t => d = v*t
t1 + t2 = 1.75
v1*t1 = v2*t2
or
t1 + t2 = 1.75
30*t1 = 45*t2
by solving the system we find
t1 = 1.05 hours
t2 = 0.7 hours
d = v1*t1 = 30*1.05 = 31.5 miles
the professors one way trip from denver to boulder is 31.5 miles.