You travel 20.0 mph for 0.500 hour, 40.0 mph for 1.00 hour, 30.0 mph for 0.500 hour, and 50.0 mph for 2.00 hours. what is the average speed?

The answer is 41.25 mph.

The average speed (v) can be expressed as:
v = D/T  
where
D is total distance: D = d1 + d2 + d3 + d4
T is total time: T = t1 + t2 + t3 + t4

Now let's calculate distances using the formula: d = v * t:
d1 = v1 * t1 = 20.0 * 0.500 = 10 mi
d2 = v2 * t2 = 40.0 * 1.00 = 40 mi
d3 = v3 * t3 = 30.0 * 0.500 = 15 mi
d4 = v4 * t4 = 50.0 * 2.00 = 100 mi

Thus, the average speed is:

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