### Brain Teasers

# Speeding Blues

Car 1 started from Point A towards point B. At the same time Car 2 started from point B towards A. They crossed each other at point C. After which, Car 1 reached point B in another 9 hrs, and Car 2 reached point A in another 4 hrs. If both the cars maintained a constant speed throughout the journey, and the speed of Car 1 was 36 miles/hr(mph), then what was the speed of Car 2?

### Answer

54 miles/hr.Here's how to solve:

Speed of Car 1 = 36 mph

Time taken from point C to B = 9 hrs

thus, distance between C to B = 36 * 9 = 324 miles (Distance = Speed * Time)

Now let the distance between point A and C be 'a' miles and let the speed of Car 2 be 'b' mph.

Thus time taken by Car 1 to travel from A to C = a/36 (Time = Distance/Speed).

and the time taken by car 2 to travel from B to C = 324/b (Distance between C and B is 324 miles as explained above)

Since both the cars meet at C, then these two times are equal, i.e.

a/36 = 324/b

or b = 324 * 36/a =11664/a

Now time taken by Car 2 to travel from C to A can be described as a/b or a*a/11664 (writing b in terms of a).

But it is given that Car 2 takes 4 hrs to travel from C to A. Thus, we get

a * a/11664 = 4

or, a * a = 46656

Now taking square root on both sides, we get a = 216. (distance cannot be negative).

Thus we get b = 11664/216 = 54.

Thus speed of Car 2 = 54 miles/hr

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