The Problem

Here's an interesting interview question I thought of on my way home from a party recently.

1. You are parked at some starting point SP which is between 2 exits E1 and E2
2. We were at a cross road with Road 1 R1 at our SP
3. Our starting point is set between exit 1 and exit 2 on the highway E1 and E2 of road 2 R2
4. To reach our destination we must reach exit 4 E4 which is past E2
5. Speed limit of R1 = 25, R2 = 50 (double)

??? When will going to E1 be faster ???

From SP at which distance is it faster to go back to E1 instead of going forward to E2.

The Solution

Show Answer

Note that:

1. D1 = D3 - D2 (i.e. D2 is always a shorter distance)
2. D2 and D1 both have the same speed (R1), D3 is double ( or .5 the distance )
3. Since R2 is 2x the speed of R1 it will take half as long to travel
4. If S1 is closer than half way then D1 will always be faster than D3 alone. Meaning the faster route is determined before the car arrives at E1
5. In the same vein, for E1 to be faster the car needs to arrive before it would have reached 1/2 * D3)
6. Since they travel at the same speed if S1 if 1/4 of the way between E1 and E2, and it would reach E1 at the same time that it would reach 1/2 * D3 (i.e. < 1/4 of D3)