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 hr, and Car 2 reached point A in another 4 hr. 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.
Explanation
Speed of Car 1 = 36 mph
Time taken from point C to B = 9 hr
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 the 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 hr 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
