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On a $20$ km tunnel connecting two cities A and B there are three gutters. The distance between gutter $1$ and $2$ is half the distance between gutter and $2$ and $3.$ The distance from city A to its nearest gutter, gutter $1$ is equal to the distance of city B from gutter $3.$ On a particular day the hospital in city A receives information that an accident has happened at the third gutter. The victim can be saved only if an operation is started within $40$ minutes. An ambulance started from city A at $30$ km/hr and crossed the first gutter after $5$ minutes. If the driver had doubled the speed after that, what is the maximum amount of time the doctor would get to attend the patient at the hospital? Assume $1$ minutes is elapsed for taking the patient into and out of the ambulance.

1. $4$ minutes
2. $2.5$ minutes
3. $1.5$ minutes
4. Patient died before reaching the hospital

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