At the local racetrack, Alex was testing the latest car.
During the eight test laps, Alex managed to average the first two laps at 100mph, the next two laps at 102mph, the next two laps at 140mph, and the last two laps at 150mph.
What was the average speed for the entire 8 laps?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
www.brainbashers.com
/puzzle/zbip
share
Hint
Remember that Time = Distance ÷ Speed, and try setting the track length to be a random length.
Answer
119mph.
Reasoning
It doesn't matter how long a lap is, so let's set the track length to be a random number, say 5 miles.
Using:
Time = Distance ÷ Speed
The first two laps took:
10⁄100 hours
The second two laps took:
10⁄102 hours
The next two laps took:
10⁄140 hours
The final two laps took:
10⁄150 hours
Therefore, the total time for the 8 laps was:
10⁄100 + 10⁄102 + 10⁄140 + 10⁄150 hours
= 1⁄10 + 5⁄51 + 1⁄14 + 1⁄15 hours
Looking at the denominators:
10 = 2 x 5
51 = 3 x 17
14 = 2 x 7
15 = 3 x 5
The lowest common multiple (LCM) of these numbers is 2 x 3 x 5 x 7 x 17 = 3570.
= 357⁄3570 + 350⁄3570 + 255⁄3570 + 238⁄3570 hours
= 1200⁄3570 hours
= 120⁄357 hours
= 40⁄119 hours
The 8 laps were 40 miles, and using Speed = Distance ÷ Time:
average speed = 40 ÷ (40⁄119)
average speed = 40 x (119⁄40)
= 119 mph
It is now four years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
