1^st Hour Topics 1 Name: ______________________________

Solving Equations

1) During a 100 mile marathon, Kim, our champion cyclist is having struggles. At the halfway checkpoint she is behind the leader, Allison, by 10 miles. Kim still has a lot of energy left and is pacing herself at a constant 15 miles per hour. Allison, on the other hand, is getting tired and has slowed down to 11 miles per hour.

a) Write an expression that relates Kim’s distance beyond the checkpoint and the number of hours that have elapsed since she passed the checkpoint.

b) Write an expression that relates Allison’s distance beyond the checkpoint and the number of hours since Kim passed the checkpoint.

c) Write an equation that represents when Allison catches up to Kim.

d) What does it mean to “solve” that equation in part c?

e) Solve the equation in part c. Explain what the answer represents,

2) Mitch is filling up a 150 gallon tank. He’s pouring the water at a rate 2.5 gallons per minute.

a) Write an expression that represents how many gallons Mitch has poured since he began.

b) Write an equation that represents the tank being half full.

c) Write an equation that represents how long it will take for the tank to be ½ full.

d) What does it mean to “solve” the equation in part c?

e) How many minutes does it take for the gallon to be ½ full?

f) How many minutes does it take for the gallon to be all the way full?

3) Two Brothers, Greg and Ethan left their home headed for New York. Greg left at 2pm and traveled at a rate of 65 miles per hour. Ethan left at 5pm and traveled at a rate of 80 miles per hour.

a) Write an expression that represents Greg’s distance traveled since he left home.

b) Write an expression that represents Ethan’s distance traveled since Greg left home.

c) Write an equation that represents when Ethan and Greg have traveled the same distance

d) What does it mean to solve the equation above?

e) Solve the equation in part c. Explain what the answer represents