Question

You and your friend leave your house at the same time to meet at a restaurant. The distance (in miles) your friend is from the restaurant is given by y=-40x+120 , 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

y = 90 - 30x is the linear equation that represents your distance from the restaurant.

Solution:

Here, the function which represents the distance between my friend and restaurant,

y = -40x + 120

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

Since, when he covered the whole distance y = 0

0 = -40x + 120

40x = 120

x = 3

Thus, he is taking 3 hours to covered the whole distance

And, According to question, me and my friend take the same time to covered the distance

Thus, the time taken by me to covered 90 miles = 3 hours

Therefore, speed is given by formula:

$speed = \frac{distance}{time}\\\\speed = \frac{90}{3} = 30$

Thus my speed is 30 miles per hour

Distance of me at "x" hour is given by:

$distance = speed \times time$

$distance = 30 \times x = 30x$

Thus, in x hour the distance between me and restaurant,

distance between me and restaurant at "x" hour = total distance - distance covered at "x" hour

y = 90 - 30x

Which is the required linear equation