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=βˆ’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.

Accepted Solution

Β y=-40x+100 This equation says your friend lives 100 miles away and travels 40 miles per hour. He takes 2.5 hours to get there.

y = -40x + 100 If y=0 then x = 100/40 = 2.5 hours and if x=0 then y=100.

You are 150 miles away and it takes you 2.5 hours to get there so your equation is:

0 = -2.5v + 150 You are solving for velocity.

v = 150/2.5 = 60 miles per hour. Now we can write the answer to the problem.

y = -60x + 150 Compare that to the original statement.

y = -40x + 100 Your buddy's speed is 40 and yours is 60. He has 100 miles to go and you have 150. Otherwise it's the same equation.