Question

You and your friend leave your houses at the same time to meet at a restaurant. The distance (in miles) your friend is from the restaurant is given by y=−50x+75, where x is the number of hours since your friend left home. You live 90 miles from the restaurant and arrive at the same time as your friend. Write a linear equation that represents your distance from the restaurant.

Answer 1

Answer:

Thus, the linear equation to represents your distance from the restaurant is given as:

$y=-60x+90$

Step-by-step explanation:

Given:

The distance (in miles) your friend is from the restaurant is given by:

$y=-50x+75$

where $x$ represents the number of hours since your friend left home.

You live 90 miles from the restaurant and arrive at the same time as your friend.

To write a linear equation that represents your distance from the restaurant.

Solution:

From the given linear equation for your friend, we can say that the distance between your friend keeps decreasing as he approaches near the restaurant. The distance will be = 0 when your friend reaches the restaurant.

Thus, we can plugin y=0 to find $x$ i.e.the time in hours taken by your frient to reach the restaurant.

$0=-50x+75$

Adding $50x$ both sides.

$0+50x=-50x+50x+75$

$50x=75$

Dividing both sides by 50.

$\frac{50x}{50}=\frac{75}{50}$

$x=1.5\ hours$

Your friend takes 1.5 hours to reach the restaurant

It is given that you and your friend start at same time  and reach the restaurant at the same time. And you are 90 miles from the restaurant initially.

The linear function representing your distance from the restaurant can be given as:

$y=-mx+90$

When you reach the restaurant $y=0$ and $x=1.5$

Plugging in values to find $m$

$0=-m(1.5)+90$

Subtracting both sides by 90.

$0-90=-m(1.5)+90-90$

$-90=-1.5m$

Dividing both sides by -1.5.

$\frac{-90}{-1.5}=\frac{-1.5m}{-1.5}$

∴ $m=60$

Thus, the linear equation to represents your distance from the restaurant is given as:

$y=-60x+90$