# Puzzle | ( Distance, Time and Work)

**Puzzle : (Distance)** There is one scooter which has 2 tyres and one Stepney (i.e. total of 3 tyres). Each tyre can run up to maximum of 5 km. How long will the scooter run?

**Solution :**

7.5 km

**EXPLANATION :**

First, ride scooter for 2.5 km and change the 1st tyre with Stepney.

Now km remaining for 1st tyre is 2.5 km , 2nd tyre is 2.5 km and Stepney is 5 km

Again ride scooter for 2.5km and this time change 2nd tyre with 1st tyre.

Now km remaining for 1st tyre is 2.5 km, 2nd tyre is 0 km and Stepney is 2.5 km

Now ride 2.5km with remaining 1st tyre and Stepney.

Total = 2.5 + 2.5 + 2.5 = 7.5km

**Puzzle : (Time and Work )** There is a room with two doors. One door empties the room in 6 minutes and the other one empties the room in 3 minutes. If both were open, how long would it take to empty the room ?

**Solution :**

2 minutes

**EXPLANATION :**

Door 1 takes 6 minutes to empty the room i.e.

1 min —— 1/6 empty

Thus, Door 1 can empty 1/6th of the people in a minute.

Door 2 takes 3 minutes to empty the room i.e.

1 min —— 1/3 empty

Thus, door 2 can empty 1/3rd of the people in a minute.

Therefore in 1 minute, both doors together can empty 1/6 + 1/3 = 1/2 of the people.

So it would take 1 more minute to evacuate the remaining 1/2 of the people.

Therefore, it takes 2 minutes to empty the room with both doors open.

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