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.