Question

A conveyor belt moves bottles at a constant speed of 120 centimeters per second. If the conveyor belt moves a bottle from a loading dock to an unloading dock, is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)(1) It takes the conveyor belt less than 1.2 minutes to move the bottle from the loading dock to the unloading dock.

(2) It takes the conveyor belt more than 1.1 minutes to move the bottle from the loading dock to the unloading dock.

Answer 1

The distance that the conveyor belt moves the bottle is less than 90 meters

Explanation:

Speed of the conveyor belt

120 cm/s

Time it takes to move the conveyor belt less than 1.2 minutes to move the bottle from the loading dock to the unloading dock.

But 60s = 1 minute

This gives

1.2 minutes = 1.2×60s seconds = 72 seconds

But speed = distance/time

so that distance = speed × time = 120cm/s ×(<72s)

From where distance = <8640cm<90m (90m×100=9000cm)

Time it takes to move the conveyor belt more than 1.1 minutes to move the bottle from the loading dock to the unloading dock.

Again 60s = 1 minute

This gives

1.1 minutes = 1.1×60s seconds = 66 seconds

Time it takes is more than 66s

But speed = distance/time

so that distance = speed × time = 120cm/s × (>66s)

From where distance >7920cm

However

7920cm < 90m (90m×100=9000cm)

So that

The distance that the conveyor belt moves the bottle is less than 90 meters