On Monday Roger drove to work in 42 minutes On Tuesday he av

On Monday, Roger drove to work in 42 minutes. On Tuesday, he averaged 5 miles per hour more, and it took him 3 minutes less to get to work. How far (in miles) does he travel to work?

Solution

Monday distance=speed x time = s x 42minutes (equal to 42/60minutes or 0.7 hours)
Tuesday distance=speed x time = (s+5mph) x (42minutes-3minutes) = (s+5) x 39 (equal to 39/60 minutes or 0.65 hours)

We know that the two distances are equal even though the speeds and times are different so we can write the following equation:
s x 0.7 hours = (s+5mph) x 0.65 hours
0.7s = 0.65s + 3.25
0.7s -0.65s = 3.25
0.05s = 3.25
s = 65 mph


Going back to the original equation:
d = s x t
d = 65mph x 0.7 hours
d = 45.5 miles