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 castings cool at the rate of 0.3°F (degrees Fahrenheit) per second and must not be allowed to cool more than 7°F before being heat treated. What is the minimum speed, in feet per second, that the conveyor must move?

Answer 1

7.07 is the answer i got as well

Explanation:

Answer 2

the minimum speed, in feet per second, that the conveyor must move is 7.07143 ft/sec

Explanation:

Let's assume time it takes to cool is 't' seconds

so, we are given

The castings cool at the rate of 0.3°F (degrees Fahrenheit) per second

so, total change in temperature will be

`=0.3* t`

`=0.3t`

must not be allowed to cool more than 7°F before being heat treated

so, that temperature must be equal to 7

`0.3t=7`

now, we can solve for t

`t=(7)/(0.3)`

`t=(70)/(3)`sec

now, we are given length of casting is 55 yards

so, firstly we will change it into ft

1 yard =3 ft

so,

`55 yard=3* 55 ft`

`55 yard=165 ft`

so, we have

total length =55 ft

now, we can use speed formula

`speed=(length)/(time)`

we can plug values

`speed=(165)/((70)/(3) )`

so, speed is 7.07143 ft/sec