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 45miles per hour.
If the round trip took 1 hour and 45 minutes, how many miles is the professor's one-way trip from Denver to Boulder?
Answer provided by our tutors
let
d = the distance of the one-way trip from Denver to Boulder
v1 = 30 mph the average speed during rush hour
t1 = the time of the trip during rush hour
v2 = 45 mph the normal average speed
t2 = the time of the trip back
the round trip took 1 hour and 45 minutes and 1 h 45 min = 1 45/60 h = 1.75 h
t1 + t2 = 1.75
since average speed = distance/time => distance = speed*time
during rush hour
d = t1*v1
d = t1*30 = > t1 = d/30
the trip back
d = t2*v2
d = t2*45 = > t2 = d/45
plug t1 = d/30 and t2 = d/45 into t1 + t2 = 1.75
d/30 + d/45 = 1.75
by solving the equation we find
d = 31.5 miles
click here to see the step by step solution of the equation
the professor's one-way trip from Denver to Boulder is 31.5 miles.