The average speed, in miles per hour, of the car for the 20 miles is 37.5 mph
Average speed
Average speed v = d/t where
- d = total distance and
- t = total time
Making t subject of the formula, we have
t = d/v
Time to cover first 10 miles
Now when the car travels 10 miles at an average speed of 30 miles per hour,
- d = 10 mi and
- v = 30 mph.
So, t = d/v
= 10/30
= 1/3 h
Time to cover next 10 miles
Also, when the car travels the next 10 miles at an average speed of 50 miles per hour,
- d' = 10 mi and
- v' = 50 mph.
So, t' = d'/v'
= 10/50
= 1/5 h
Time to cover 20 miles
The total time for the 20 miles is T = t + t'
= 1/3 h + 1/5 h
= (5 + 3)/15 h
= 8/15 h
Average speed for 20 miles
So, the average speed for the 20 miles is v = D/T where
- D = 20 miles and
- T = 8/15 h.
So, v = D/T
v = 20 mi ÷ 8/15 h
v = 20 × 15 mi/8 h
v = 2.5 × 15 mi/h
v = 37.5 mph
So, the average speed, in miles per hour, of the car for the 20 miles is 37.5 mph
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