Question

At the metal-casting company where you work, you must set up a conveyor system to move castings from the furnace to the heat treatment area 55 yards away. The casting cools at the rate of 0.3F per second and must not be allowed to cool more than 7F before being heat treated. What is the minimum speed, in feet per second, that the conveyor must move?

Answer 1

The minimum speed at which the conveyor must move is approximately 7.08 feet per second.

Step-by-step explanation:

To calculate the minimum speed that the conveyor must move, we need to determine the maximum time it takes for the casting to cool by 7°F. Since the cooling rate of the casting is 0.3°F per second, we divide 7°F by 0.3°F/second to find the maximum time in seconds:

t = 7°F / 0.3°F/second = 23.33 seconds.

Since the distance is given in yards, we need to convert it to feet: 1 yard = 3 feet. So, the distance is 55 yards x 3 feet/yard = 165 feet.

The minimum speed of the conveyor can be calculated by dividing the distance by the maximum time:

speed = distance/time = 165 feet / 23.33 seconds ≈ 7.08 feet per second.