# Puzzle :: Calculate total distance travelled by Bee

Puzzle: Two trains are on same track and they are coming toward each other. The speed of the first train is 50 km/h and the speed of the second train is 70 km/h. A bee starts flying between the trains when the distance between two trains is 100 km. The bee first flies from first train to second train. Once it reaches the second train, it immediately flies back to the first train … and so on until trains collide. Calculate the total distance travelled by the bee. given that Speed of bee is 80 km/h.

1. Let the first train A move at u km/h.
2. Let the second train B move at v km/h.
3. Let the distance between two trains be d km
4. Let the speed of bee be b km/h

## What is speed?

Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.

The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this puzzle, distance is in kilometres (m) and time is in hours(s), so the units will be in kms per hr (kms/hr).

## Rearranging the formula

The formula speed = distance ÷ time can be rearranged, just like any other equation.
The formula can be rearranged in three ways:
• speed = distance ÷ time
• distance = speed × time
• time = distance ÷ speed
To calculate one of the variables (speed, distance or time) we need the other two.

Therefore, the time taken by trains to collide in this puzzle =  distance / speed

here distance is d and speed is sum of speed of train A and train B which is u+v
hence, time taken by trains to collide = d/(u+v)
Now putting all the known values into the above equation, we get,

u = 50 km/hr
v = 70 km/hr
d = 100 km
b = 80 km/hr

Therefore, the total distance travelled by bee
distance = speed × time

we know that Speed of bee is 80 km/h and total time bee travels is d/(u+v) after substituting, the equation becomes

distance = b*d/(u+v)
substituting the values of b d u and v,
equation becomes

= 80 * 100/(50+70)
= 66.67 km (approx)

thus total distance travelled by bee is - 66.67 km approx.

Puzzle 2 : There are two trains(Train A and Train B) running on the same track towards each other at a speed of 100 km/hr. They enter a tunnel 200 km long at the same time. As soon as they enter, a supersonic bee flying at a rate of 1000 km/hr also enters the tunnel from one side (say Train A side). The bee flies towards the other Train B and as soon as it reaches the train B, it turns back and flies back to the Train A. This way it keeps flying to and fro between the Trains A and B. The trains collide after a certain point of time leading to a massive explosion. The task is to find the total distance travelled by the bee until the collision occurred.

Solution:

This puzzle can be solved with the help of physics and observation.

• Speed of Train A and Train B = 100 km/hr
• Length of the tunnel = 200 km
• Since both the trains are travelling at the same speed, Hence they must have travelled equal distance before colliding, which means that they must have collided at the halfway of the tunnel.
• Therefore, distance travelled by each train before colliding = 100 km
• Time taken by each train to travel 100 km and collide = Distance/Speed = 100/100 = 1 hr
• Therefore the bee must have travelled for 1 hr before colliding with the trains.
• Hence distance travelled by the bee in 1 hr before colliding = Speed * Time = 1000 * 1 = 1000 km
thus total distance travelled by the bee until the collision occurred is 1000 km.