relating potentiometer to time

hi I am totally new to Arduino and am learning the analog input using a potentiometer and LEDs, where you control the LED on off with a potintiometer.

I want to go one step further and link the the min and max of my potentiometer to time lets say 0 to 60 second. Can some one help me please.
I tried to use the map function to achive this but was unsuccessful can some one please guide me on how to.

void loop() {
// read the value from the sensor:
sensorValue = analogRead(sensorPin);
// turn the ledPin on
digitalWrite(ledPin, HIGH);
// stop he program for milliseconds:
map(sensorValue, 0,1023,0 millis, 60000 millis);
delay(sensorValue);
// turn the ledPin off:
digitalWrite(ledPin, LOW);
// stop the program for for milliseconds:
delay(sensorValue);
}

Is the difference between 60000 and 60 * 1023 critical? If not, don't piss away resources on mapping (incorrectly) the sensor reading. Simply multiply it by 60, making sure that overflow doesn't happen (by using the appropriate type of variable to hold the sensor reading).