Track
A man is riding a bike around a racetrack. A horse running around the track
in the same direction at 15 mph passes him at intervals of two minutes.
Another horse running at 21 mph in the same direction passes him at
intervals of one minute. Find the speed of the bike.
The answer is 9.
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1 solution
Using the Distance, Speed and Time relationship we can solve this problem where Distance=Speed * Time
The horse that runs in the same direction as the bike with speed v passes him at intervals of 2 minutes or 2/60 hr. In 2/60 hour, the bike would have gone v * 2/60 miles. Hence, the horse would also have completed a complete circle of the track, x miles, plus the additional v* 2/60 miles. Therefore, it took the horse to traverse (x+ v(2/60))/15 miles in 2/60 hour. Rewriting this, (x+v(2/60))/15=2/60 ( equation 1)
Now, do the same for the other horse running at 21 mph and passing the bike at 1/60 hour intervals. We have (x+v(1/60))/21=1/60 ( Equation 2)
Solving for these 2 simultaneously, we obtain x=1/5 miles and v=9 mph