Algebra Word Problem: need help?

Question

Michael drove to a friends house at a rate of 40mi/h. He returned by the same route at a rate of 45 mi/h. the driving time for teh round trip was 4h. What is the distance Michael traveled?

Answer 1

The total round trip distance is d.  Each leg is d/2.  The time to travel both legs was

d/2/40 + d/2/45 = 4

d/80 + d/90 = 4

90d + 80d = 4*7200

17d = 2880

d = 2880/17 = 169.4 (approx) miles

Check: driving time leg 1 + leg 2

169.4 / 2 / 40 + 169.4 / 2 / 45 = 2.12 + 1.88 = 4.00 hr

Answer 2

I solved this using a one-variable equation.  

x/40 + x/45 = 4 because distance divided by rate is time.  

45x + 40x = 4(40)(45) getting a common denominator

85x = 7200 simplify

x = 84.71 by division

double it to get the WHOLE distance (both ways combined): 169.42mi