Find the Equation
Rates
Real-world Situations
Motion on the number line
When will they meet?
100

The equation relating t and y for the points (1,-4), (3,2), (5,8), (7,14)

What is y=-4+3(t-1)?

100

The number of gallons of water that will be added to a pool by t=45 if a hose fills at a rate of 16 gal/min.

What is 720 gallons? 

100

Harry saves $40/week, starting with $100. Write an equation for his savings.

What is S=40t+100?

100

The position equation for point A that starts at -25 and moves right 6 units/sec.

What is A=6t-25?

100
Josh hikes at 2.4 mph and Vaughn at 3.2 mph from opposite ends of a 14 mile trail. This is when they meet. 

When is 2.5 hours? 

200

The linear equation relating t and Q for (4,100), (7,98), (10,96), (13,94)

What is Q=100-2/3(t-4)?

200

A tank has 42 gallons and leaks 3 gallons every 4 hours. This is the number of gallons that are left after 31 hours. 

What is 18.75 gallons? 

200

Pepsi Stadium cools from 72°F to 48°F at a rate of 4°F per 15 minutes. This is how long it takes.

What is 90 minutes? 

200

Point C starts at 100 and moves left 4 units/6 sec starting at t=5. Find its position equation. (Be sure to reduce!)

What is C=100-2/3(t-5)?
200

This is where along the trail Josh and Vaughn meet.

What is 6 miles? 

300

Write an equation for G if a hose fills a pool at 16 gallons/minute and G=3000 when t=30

What is G=3000+16(t-30)

300

The rate of change for the following points: (2 hours, 1968 oranges), (6 hours, 3504 oranges).

What is 384 oranges per hour? 
300

Students leave school at a rate of 3.5 students/minute. 125 remain in the school at 20 minutes. This is how many remain at 30 minutes.

What is 90 students?

300

The rate of motion in units per second for a particle moving from 70 to 50 over 4 seconds.

What is -5 units per second? 

300

Point A starts at -25 and moves right 6units/sec. Point B starts at 99 but stays still for 3 seconds, then moves left 4 units/second. This is when they collide. 

When is 13.6 seconds? 

400

Write an equation for the number of students S leaving school starting at 360 and decreasing by 30 students/minute.

What is S=-30t+360? 

400

Write a linear equation for the distance away from you if a person starts 14 miles away and walks at a rate of 3.2mph.

What is d=-3.2t+14? 

400

Orange workers store 3504 oranges after 6 hours. Assuming they start with 0 oranges stored, this is how many oranges are stored at 4.5 hours.

What is 2,628 oranges? 

400

The position equation for point B if it stays at 99 for 3 seconds, then moves left at a rate of 4 units/sec.

What is B=99-4(t-3)?

400

This is the position point A and point B will be at when they collide. 

What is 56.6? 

500

Find the equation for the location of a particle if P=70 at t=8 and P=50 at t=12

What is P=70-5(t-8)?

500

A point moves right at a rate of 6 units/3 seconds. Write its position equation if it starts at -6.

What is p=2t-6?

500

A 42 gallon tank leaks out completely at a rate of 3 gallons every 4 hours. This is how long it takes.

What is 56 hours? 

500

The moment when points A and B collide if A starts at -25 and moves right 6 units per second, and B starts at 99 and moves left 4 units per second, but only starts moving at t=3.

When is 13.6 seconds? 

500

Two workers harvested 1968 oranges after 2 hours and 3504 after 6 hours. They stop when there are 4368 oranges. This is how long their workday is.

What is 8.25 hours?