# If a tire rotates 150 revs/min when a truck is travelling 40km/h, what is the circumference of the tire?

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Given that the tire rotates 150 revs/ min

Also, given that the truck is traveling 40 km / h

First we will determine how many m / min the truck travels:

(40km/h) x (h/60min) = (2/3)km/min

==> We know that :

1 km = 1000m

==> (2/3) km / min = (2000/3) m / min

Now we will calculate the circumference of the tire:

Let x be the circumference of the tire:

(150revs/min) (x m/rev) = 2000/3 m/min

150x = 2000/3 m/min

x m = 2000/450 = 4.4

x = 4.4 meters

**Then the circumference of the tire is 4.4 m **

Given:

Speed of truck = 40 km/H = 40*1000 = 40,000 m/h

Rotational speed of tire = 150 rev/min = 150*60 = 9,000 rev/h

For each rotation of a tire the truck moves by a distance equal to the circumference of the tire.

Therefore the circumference of the tire is equal to:

Circumference = (Speed of truck)/(Rotational speed of tires)

Substituting the given values of speed of truck and rotational speed of tires in the above equation:

Circumference = 40,000/9,000 = 4.4444 m

Answer:

Circumference of tire = 4.4444 m.

The number of rotations of the tyre per minute = 150 reveloutions/ minute.

The speed of the truck = 40km/hour.

Therefore the distance covered by the truck per minute = 40 km /60 min = 40000m/60 = 2000/3 m . Therefore the wheel moves by 2000/3 m in 150 revlutions.

Therefore the in one revolution the wheel moves by a distance (2000/3)/150 m = 40/9 meter = 4.44 meter.

Since the distance moved by one rotation of the wheel is equal to the circumference, 4.4m is circumference of the wheel.