Expert: Scott A Wilson - 10/27/2009

Question
I need help doing these two problems. I have a software of SAT Prep and it gave me these two problems but I did not understand its explanation:

1.)     A car traveled from A to B at an average speed of 40 miles per hour and then immediately traveled back from B to A at an average speed of 60 miles per hour. What was the car's average speed for the round trip, in miles per hour?
I got 50 mph, but its wrong.

2.)     How many positive integers less than 100 contain one or more of the digits 3, 5, and 8?
I got 30, then 33. But both of my answers are wrong.  

Answer
The distance from A to B is x.
At 40 mph, this takes x/40 hours to drive.
At 60 mph, this takes x/60 hours to drive.
Thus, the total time is x/40 + x/60 = 3x/120 + 2x/120 = 5x/120 = x/24.

Yet lets put all the time in 120ths.
That is, at 40mph it took 3x/120 hours; at 60mph, it took 2x/120 hours,
and the total time was 5x/120 hours.

The average is then ((40)(3x/120) + (60)(2x/120))/(5x/120).
Now multiply by (120/x)/(120/x) to cancel x out and the result is
(40•3 + 60•2)/5 = (120+120)/5 = 240/5 = 48.