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

Answer:

x = 35.25 hr

Step-by-step 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

$x=\frac{3}{4}y-\frac{9}{4}$

Now, we have to find x for y = 50

Replace y with 50

$x=\frac{3}{4}\cdot50-\frac{9}{4}\\\\x=\frac{75}{2}-\frac{9}{4}\\\\x=\frac{141}{4}\\\\x=35.25$

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