Choose some smart number for the distance from Mayville to Rome: let the distance be 120 miles (120 is LCM of 30 and 40 and this will make further calculations easier).

\(Average \ speed=\frac{total \ distance}{total \ time}\) --> so the nominator, total distance would be \(2*120=240\);

Total time equals time from Mayville to Rome plus time from Rome to Mayville --> \(\frac{120}{30}+\frac{120}{40}=7\);

\(Average \ speed=\frac{total \ distance}{total \ time}=\frac{240}{7}\approx{34.3}\).

Answer: C.
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It is pretty involuntary to come up with 35 miles per hour as the average speed in this case. But, that is wrong. Since, the car has taken more time to travel at 30 mph and less time to travel at 40 mph, the avg speed of the car would be somewhere between 30 and 35(mean) and closer to 35. If I had no time on my hands and had to make a calculated guess, I would have chosen C.

The correct way to find the avg speed is to calculate the total distance and the total time and divide the total distance by total time.

Let the one way distance in this case be D. So the total distance is 2D(travelled over the same route twice)

Total Time = Time taken to travel distance D at 30 mph + time taken to travel distance D at 40 mph
= \((D/30) + (D/40)\)
= \(7D/120\)
Thus avg speed = Total distance/total time
= \((2D)/(7D/120)\)
= 34.285

Hope it helps,
meshtrap

This is just an approximation and round trip problem- we simply pick a value- which is usually the LCM

Total Distance= Avgspeed * Total Time

120/30= 4
120/40= 3

240= average speed * 7

240/7= 34.3

We can use the average rate formula: average = total distance/total time, and let the distance each way = 120 miles. (Note that we could use any number for the distance, but we have chosen the convenient number 120 because it is evenly divisible by both 30 and 40, making the arithmetic easier.)
average = 240/(120/30 + 120/40)

average = 240/(4 + 3) = 240/7 = 34.3

Answer: C
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For Avg speed if two speeds are given formula is Avg speed=2*S1*S2/S1+S2=34.2

If the distance is equal in both trips, then
Average speed =2xy/(x+y)
=2*30*40/70
=34.3 miles/hr
x=speed in first trip
y= speed in second trip