Question

A physicist working in a large laboratory has found that light particles traveling in a particle accelerator increase velocity in a manner that can be described by the linear function −4x + 3y = 9, where x is time and y is velocity in kilometers per hour. Use this function to determine when a certain particle will reach 50km/hr.

The particle will reach 50km/hr when x =
.

Answer 1

The particle will reach 50km/hr when x = 35.25 hours

Answer 2

x = 35.25 hr

Explanation:

The velocity model is given by −4x + 3y = 9, where x is time and y is velocity in kilometers per hour.

Solve the equation for x

Add 4x to both sides of the equation

`3y=4x+9`

Subtract 9 to both sides

`3y-9=4x`

Divide both sides by 4

`x=(3)/(4)y-(9)/(4)`

Now, we have to find x for y = 50

Replace y with 50

`x=(3)/(4)\cdot50-(9)/(4)\\\\x=(75)/(2)-(9)/(4)\\\\x=(141)/(4)\\\\x=35.25`

Therefore, the particle will reach 50 km/hr when x = 35.25 hr