# Double Number Line/ Unit Rate Problems

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1 Rate and Unit Rate Word Problems (with Answers) 6.RP Support Material Page 1 of 6 Basic Reviews Rate and Unit Rate Word Problems (with Answers) Double Number Line/ Unit Rate Problems 1. Amy drove to her mother s house, which is 204 miles away. If it took her 3 hours, what was her average speed? 204 miles/3 hours = 68 miles per hour 2. Four gallons of gasoline cost \$ What is the price per gallon? \$16.80 / 4 gallons = \$4.20 per gallon 3. A T-shirt launcher can launch 5 shirts in 20 minutes. What is the rate in shirts per hour? 5 shirts 20 minutes Multiply both by 3 to get to 60 minutes 15 shirts 60 minutes 15 shirts per hour

2 Rate and Unit Rate Word Problems (with Answers) 6.RP Support Material Page 2 of 6 Two- Step Rate Problems: Asking for more! 4. Four gallons of gasoline cost \$ (a) What is the price per gallon? \$16.80 / 4 gallons = \$4.20 per gallon (b) What is the price of gasoline in terms of gallons per dollar? 4 gallons /\$16.80 = 0.24 gallons per dollar (c) Do we need both rates? In real life, when will they become useful? Yes. Both rates can be useful. (1) \$4.20 /gallon is useful when you know how much gasoline you need and want to find out how much it cost. (2) 0.24 gallon/dollar is useful when you know how much money you have and want to find out how many gallons of gasoline you can buy with that amount of money. 5. Ashley needs to ride her bike to her friend s house 96 miles away. She is riding at an average rate of 15 miles per hour. She has 6 hours to get there. Will she make it? 96 miles / 15 miles per hour = 6.4 hours. She will not make it in 6 hours. 6. Ed drives from Jefferson to Holden, a distance of 250 miles. He then travels on to Paxton, which is 50 miles from Holden. If it takes him 5 hours to complete the entire trip, how fast is he traveling if he is traveling at a constant speed? 250 miles + 50 miles = 300 miles 300 miles / 5 hours = 60 miles per hour 7. Which is the best buy? 6 shirts for \$ shirts for \$ shirts for \$21 \$25.50 / 6 shirts = \$4.25 per shirt \$18.00 / 4 shirts = \$4.50 per shirt \$21.00 / 5 shirts = \$4.20 per shirt- this is the best buy

3 Rate and Unit Rate Word Problems (with Answers) 6.RP Support Material Page 3 of 6 8. Lauren took 12 hours to read a 360 page book. At this rate, how long will it take her to read a 400 page book? 360 pages / 12 hours = 30 pages per hour400 pages / 30 pages per hour = 13 1/3 hours = 13 hours and 20 minutes 9. Pat wants to enter a typing contest. In order to enter, one has to be able to type 50 words per minute. Pat took 15 seconds to type 10 words. Can he enter the contest? 10 words 15 seconds Multiply both by 4 to reach 60 sec, then convert to min40 words 1 minute Pat cannot enter the contest

4 Rate and Unit Rate Word Problems (with Answers) 6.RP Support Material Page 4 of 6 Differentiated Rate Problems: Choose the level for your students- Part a: Basic Review Part b: Asking for more Part c: Stepping beyond 10. Five lemons cost \$1.80. a. What is the cost per lemon? \$1.80 / 5 lemons = \$0.36 b. At this rate, what is the cost of 9 lemons? \$0.36 x 9 lemons = \$ David hikes 2 ¼ miles in ½ an hour. a. What is his rate in miles per hour? 2 ¼ miles = ½ an hour Multiply both sides by 2 to convert to hours 4 ½ miles = 1 hour David hikes 4 ½ miles per hour b. At this rate, how long will it take him to walk 18 miles? 18 miles / 4.5 miles per hour = 4 hours c. If he walks for 7 hours, how far will he have gone? 4.5 miles per hour x 7 hours = 31.5 miles 12. Erica babysits for 4 ½ hours and is paid \$27. a. How much does she make per hour? \$27 / 4.5 hours = \$6 per hour b. How much does she make for 8 hours? \$6 per hour x 8 hours = \$48 c. If the people she babysits for have \$34 to pay her, how long can they stay out? \$34 / \$6 per hour = 5 2/3 hours = 5 hours and 40 minutes

5 Rate and Unit Rate Word Problems (with Answers) 6.RP Support Material Page 5 of Michael is headed to his aunt s house. For the first 2 hours he drives at 55 mph. For next hour, he drives 70 mph. For the final 2 hours he drives 50 mph. a. How far does he travel? 55 miles per hour x 2 hours = 110 miles 70 miles per hour x 1 hour = 70 miles 50 miles per hour x 2 hours = 100 miles 110 miles + 70 miles miles = 280 miles b. What is his average speed for the entire trip? 2 hours + 1 hour + 2 hours = 5 hours 280 miles / 5 hours = 56 miles per hour c. If he drives the entire trip at 70 mph, how much less time will it take? 280 miles / 70 miles per hour = 4 hours 5 hours 4 hours = 1 hour less 14. John took a 5 ½ mile walk to his friend s house. He left at 11 a.m. and arrived at his friend s house at 1 p.m. a. What was his average speed of walking? 5 miles / 2 hours = 2 miles per hour b. If the return trip took a half hour longer, how much lower was his average speed on the return trip than on the trip to his friend s house? 5 miles / 2 hours = 2 miles per hour 2 miles per hour 2 miles per hour = miles per hour

6 Rate and Unit Rate Word Problems (with Answers) 6.RP Support Material Page 6 of Tom jogged from 10:30 a.m. to 12:15 p.m. He traveled a distance of 7 miles. a. What was his average rate of jogging? 7 miles / 1 hours = 4 miles per hour b. At 12:15 p.m., he decided to go an additional 5 miles at the same rate. At what time should he finish the additional 5 miles? 5 miles / 4 miles per hour = 1 hours more, he finished at 1:30 p.m.

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