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

Answer:

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

Step-by-step 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

$=0.3\times t$

$=0.3t$

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

$t=\frac{7}{0.3}$

$t=\frac{70}{3}$sec

now, we are given length of casting is 55 yards

so, firstly we will change it into ft

1 yard =3 ft

so,

$55 yard=3\times 55 ft$

$55 yard=165 ft$

so, we have

total length =55 ft

now, we can use speed formula

$speed=\frac{length}{time}$

we can plug values

$speed=\frac{165}{\frac{70}{3} }$

so, speed is 7.07143 ft/sec

Answer 2

Answer:

7.07 is the answer i got as well

Step-by-step explanation: