Michael drove to a friend’s house at a rate of 40 mi/h. he returned by the same route at a rate of 45 mi/h. the driving time for the round trip was 4 h. what is the total distance michael traveled?

169.41 mi

Step-by-step explanation:

Let the time required for the outbound trip be t1 and that for the inbound (return) trip be t2.  Then t1 + t2 = 4 hr.  We can eliminate one variable by solving this equation for it:  t1 = 4h - t2.

Then the time spent on the outbound trip was t1 = d / (40 mph) and that on the inbound trip t2 = d / (45 mph).  We want to find the total distance traveled, which will be 2d.

                                              d                    d

t1 + t2 = 4 hr becomes   +  =  4 hr  

                                          40 mph        45mph

We must solve for d.  The LCD here is 40*45, or 1800; thus, this equation becomes  

   45d + 40d = 4(1800), or 85d = 7200.  Thus, d = 84.7 miles.

Michael drives this same distance going and returning, so the total distance he drives is 2(84.7 miles) = 169.41 mi