Two bicyclists travel at a constant rate of 15 mph directly toward each other. W
ID: 1529286 • Letter: T
Question
Two bicyclists travel at a constant rate of 15 mph directly toward each other. When they are 25 miles apart, a bumble bee flies from the front wheel of one bike directly to the wheel of the other bike at a rate of 25 mph. It touches it and turns around in a negligibly short time and returns at the same speed to the first bike, whereupon it turns around instantaneously and repeats the back and forth trip over and over again-successive trips becoming shorter and shorter until the bikes collide and squash the unfortunately bee between the front wheels. What is the total mileage of the bee in its many back and forth trips from the time the bikes were 25 miles apart until its hapless end?
(Please include the diagram along with the solution)
Explanation / Answer
D = distance between the bicyclists = 25 miles
V = relative speed = 15 + (-15) = 30 mph
t = time taken for the bikes to collide = D/V = 25/30
Vb = speed of the bee = 25 mph
distance travelled by the bee
Db = Vb t
Db = 25 (25/30) = 20.83 miles