Activities

1. When Josh is driving 55 miles per hour, how long will it take him to drive 400 miles?

2. What is the rate of change in Matt’s bank account if he spent $367 dollars more than he earned over the past 5 months?

3. When building a house a carpenter determines that the roof should go up six inches for every foot of lateral distance. What is the elevation change for a 10 foot lateral distance of roof?

4. What is the rate of change for a river that falls 300 feet over a distance of 3 miles?

5. A unicycle’s tire completes a full revolution 3,000 times during a 4-hour bike ride. How many revolutions per minute does the tire make?

6. An alpine mountain climber goes uphill at a much slower rate than she climbs downhill. If it takes her 12.5 hours to ascend at a rate of 1,000 feet of elevation per hour and she descends in only 8 hours, what is her rate of descent?

7. Dan reads his favorite series of books at a rate of 19 pages per hour. If Dan has already read the series for 34 hours but still has 1193 pages left, how many pages are in the series altogether?

8. Two basketball players are trying to have the most points per game for the season. The current leader has 2112 points in 77 games and the second place player has 2020 in 74 games. Assuming the current leader plays no more games, how many points per game will the second place player have to score in the next three games to take the lead in this category?

9. A train left Philadelphia at 8 AM on July 1^st. It traveled 2,864 miles to Portland, Oregon, arriving at 9AM on July 4^th. What was the average rate of change of the train in miles per hour?

10. A rocket ship is 1 mile above the earth’s surface after 15 seconds of travel. It is 5 miles above the surface of the earth after 2.5 minutes. What is the rocket’s average rate of change during that time period?

11. Joey is eating his favorite type of potato chips as part of his lunch. Joey opened a new bag which had 143 chips remaining after 3 minutes and 91 chips left after 7 minutes. Assuming Joey always ate the same number of chips per minute, how many potato chips were in the bag originally?

12. A portrait artist can complete a 250 in² picture in 5 hours and a 100 in² picture in 3 hours. At that same rate, how long would it take her to complete a much larger 500 in² portrait?

13. One of your horses eats 20 lbs. of hay per day while your other horse eats about 30 lbs. of hay per day. If you already have one hundred bales of hay that weigh 45 lbs. each, how many more 45 lb. bales will you need for both of your horses to last through the next 6 months?

14. What is the rate of change between the original price of an item at the store and the price after 6% sales tax?

15. Brian’s hair grows at a rate of  inches per day. Brian likes to get his hair cut every time it grows 1.5 inches since the last haircut. How often does Brian need to plan to get his hair cut?

16. The number of people living in a small town in the Northern Tier of Pennsylvania is 1,561 in 2014. Back in 2007 there were only 1,274 residents in the town. If the population rate of change remains steady, how long will it take the population to double from its 2014 size?

17. A car is traveling according to the distance versus time graph below. Explain the car’s rate of change during each different segment of the graph.

18. A certain math teacher likes to calculate the rate at which he can do the dishes after a meal at his house (unfortunately he does not have a dishwasher). He knows that he can wash silverware at a rate of 10 pieces per minute. He can wash dishes (plates, cups, etc.) at a rate of 5 pieces per minute. How long would it take him to wash 14 dishes and 18 pieces of silverware?

19. Jacob’s investments grew from $12,453 to $17,891 during a three month time period. Unfortunately, during the next month he lost $5438 worth of investments in a stock market crash. What was Jacob’s rate of change per month for (a) the first three months, (b) the fourth month, and (c) all four months?

20. A set of stairs goes up 3 feet for every 5 stairs. How many stairs are required for a set of stairs to go up 11 feet?

21. A peregrine falcon can plummet for short distances at a rate that would allow them to travel from Philadelphia to Pittsburgh, a distance of 305 miles, in one hour and twenty minutes. How long would it take a falcon to plummet one mile?

22. When the input of a linear function increased from -7 to 15, the output decreased from 23 to -19. What is the output of the function when the input is zero?

23. On the graph below each unit in the x direction represents 5 months of time since Nick started a checking account and each unit in the y direction represents $100 in Nick’s checking account. Determine how many months it will take until Nick’s account has $0.

24. A tornado is expected to arrive at a town in approximately 4 minutes. A car notices the storm 100 miles behind it and speeds towards the town at 80 mph arriving 1 minute before the tornado to warn everyone. How fast was the tornado traveling?

25. Two runners are approaching the finish line of a race. The first runner is 2 miles away and running at a speed of 8 miles per hour. The second runner is 3 miles away and running at a speed of 7 miles per hour. How much time will it take from when the first runner finishes until the second runner finishes?

Answer Key/Rubric

1. 7.27 hours

2. -$73.40 per month

3. 5 feet

4. -0.0189 or down 1 foot per 52.8 feet of lateral distance

5. 12.5 revolutions per minute

6. -1562.5 feet per hour

7. 1839 pages

8. 31 points per game

9. 39.23 miles per hour

10. 1.78 miles per minute

11. 182 chips

12. 6 hours and 40 minutes

13. About 100 bales of hay

14. 1.06

15. Every 90 days or 3 months

16.  Between the years 2052 and 2053

17. During the first minute the car is driving away at a constant rate. During the second minute the car is stopped (at a red light?). During the third minute the car is driving away faster than before. During the fourth minute the car is driving back towards where it started very slowly. During the last minute the car is stopped again.

18. About 4 minutes and 39 seconds

19. (a) + $1812.66 per month
    (b) - $5438.00 per month
    (c) $0 per month

20. 19 stair

21. 15.65 seconds

22. About 9.64

23. 130 months

24. 105 miles per hour
    
    
25. Approximately 10.7 minutes later