Bill drove from Ajax to Bixby at an average speed of 50mi/h. On the way back, he drove at 60mi/h. The total trip took 4 2/3 hours of driving time. Find the distance between the two cities.

Answer 1

Let the distance between the two cities be d.
The time it took for Bill to drive from Ajax to Bixby is d/50.
The time it took for Bill to drive from Bixby back to Ajax is d/60.
The total driving time is d/50 + d/60.
The total driving time in hours is 4 2/3 = 14/3 hours.
So, d/50 + d/60 = 14/3.
To get rid of the denominators, we can multiply each term by 150 (the LCM of 50 and 60).
3d + 2d = 14 * 50.
5d = 700.
Thus, the distance between the two cities is d = 700/5 = <<700/5=140>>140 miles. Answer: \boxed{140}.