At precisely midnight, Dracula leaves Chicago bound for Atlanta and flying at 50 mph. Two hours later, Lucadra leaves Atlanta bound for Chicago and flying at 70 mph. Dracula and Lucadra are travelling on parallel flight paths, and the distance between Chicago and Atlanta, as the vampire flies, is 716 miles. When the two vampires pass each other, which will be further from Atlanta?



No calculations are required to answer this question, but it does require a little mental gymnastics.

Imagine a flight path 716 miles long. At one end is Chicago; at the other end is Atlanta. Regardless of the point (i.e., at 1, 2, 3 or 4) where Dracula and Lucadra fly past each other, they will both be the same distance from either Chicago or Atlanta.

(1)    (2)    (3)    (4)
<-L    <-L    <-L    <-L
D->   D->   D->   D->
l-------------------------------------------------------------l
CHICAGO                                              ATLANTA

If you like playing with numbers, however, it is possible to determine when and where Drac and Luc will whizz past each other. For example, by calculating how far each vampire flies with each passing hour, it is possible to estimate approximately where they will meet. By making a few more calculations, it is even possible to determine the exact time and mileage marker at which they will pass each other.

But wait. There's actually an easier way to find out exactly where Lucadra and Dracula zip past each other without going through these cumbersome and repetitive calculations.

How long a moving body takes to travel a particular distance is determined by the distance and the speed at which it is moving. Dracula is moving at 50 mph and must travel 716 miles, therefore it will take him 716mi/50mph = 14.32 hours to fly all the way to Atlanta. Lucadra must also travel 716 miles, but she is flying at 70 mph, therefore it will take her only 716mi/70mph = 10.23 hours to fly to Chicago. But Dracula began his flight at noon, while Lucadra begins hers two hours later. In short:

Vampires Speed x Time = 716 miles

Dracula    50 x T = D

Lucadra    70 x T-2 = D

To determine the time at which they will meet during their 716 mile flights, set up an equation in which Dracula's unknown distance is 50mph x Ti (or 50T), and Lucadra's unknown distance is 70mph x T-2 (or 70(T-2)). The total distance covered by both together must be 716 miles.

Dracula's D + Lucadra's D = 716 miles

50T + 70(T-2) = 716

50T + 70T - 140 = 716

120T = 716 + 140

120T = 856

T = 7.13333 hours (Dracula)

T-2 = 5.13333 (Lucadra)

At 7.13333 hours, Dracula will have flown 7.13333hrs x 50mp = 356.67 miles toward Atlanta, leaving him 716 - 356.67 = 359.33 miles to go. At that same time, Lucadra will have flown 5.13333hrs x 70mph = 359.33 miles away from Atlanta, so they will both meet at the 356.67 mile marker, and the time will be 7 hours and .13333 x 60 = 8 minutes, or 7:08 PM.

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