Answer:
36 mph
Step-by-step explanation:
The appropriate relations are ...
time = distance/speed
speed = distance/time
Suppose the race has a total length of 360 miles. Then half the race is 180 miles.
The cyclist's time on the first half is (180 mi)/(30 mi/h) = 6 h.
The cyclist's time on the second half is (180 mi)/(45 mi/h) = 4 h.
The total time is 10 h for the total distance of 360 mi, so the average speed is ...
(360 mi)/(10 h) = 36 mi/h
_____
The length of the race doesn't matter. The above numbers make the math convenient. The average is computed from ...
1/((1/2)/30 + (1/2)/45) = 2/(1/30 +1/45) = 2·30·45/(30+45) = 36
This is the <em>harmonic mean</em> of the numbers 30 and 45.
