Question

You and your friend leave your houses at the same time to meet at a restaurant . The distances(in miles) your friend is from the restaurant is given by y=-40x+100, where x is the number of hours since your friend left home. You live 150 miles from the restaurant and arrive at the same as your friend. Write a linear equation that represent your distance from the restaurant

Answer 1

The equation that represents your distance from the restaurant is $y=-60x+150$

Explanation:

The distance covered by your friend is $y=-40x+100$

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

Since, your friend traveled the whole distance, we can find the time taken to travel the whole distance by equating $y=0$

Thus,

$\begin{array}{r}{40 x=100} \\{x=\frac{100}{40}} \\{x=2.5}\end{array}$

Thus, the time taken by your friend to travel the whole distance is 2.5 hours.

It is given that, you and your friend take the same time to travel the distance, thus, the time taken by you to cover the distance of 150 miles is 2.5 hours.

To find the speed, let us use the formula $speed=\frac{distance}{time}$

Substituting the values, in this formula,

$speed=\frac{150}{2.5}=60$

Thus, the speed is 60 miles.

Hence, the distance covered by you to reach the restaurant is given by

$y=-60x+150$