# The Problem

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

- You are parked at some starting point
`SP`

which is between 2 exits`E1 and E2`

- We were at a cross road with Road 1
`R1`

at our`SP`

- Our starting point is set between exit 1 and exit 2 on the highway
`E1 and E2`

of road 2`R2`

- To reach our destination we must reach exit 4
`E4`

which is past`E2`

- 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

### Note that:

`D1 = D3 - D2`

(i.e. D2 is always a shorter distance)`D2`

and`D1`

both have the same speed (`R1`

),`D3`

is double ( or .5 the distance )- Since
`R2`

is 2x the speed of`R1`

it will take half as long to travel - 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`

- In the same vein, for
`E1`

to be faster the car needs to arrive before it would have reached`1/2 * D3`

) - 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`

)

# In Conclusion

Its about how the interviewee answers the question, not the answer they give.

So, take note of the interviewees thought process while solving the problem.

**Remember:** The question is better when you word it like I did.

Do not say *Which route is faster*.

That is not the question, it is *When is going backward faster*.

This will force the interviewee to use a logical thought instead of a geometrical.