5.2 – Real-World Problems: Rates and Unit Rates

Objective…

Part A:Solve simple word problems involving rates and unit rates

1)A machine can pack 70 boxes of spaghetti in 5 minutes.

Bar Model / Math Statement
  1. At this rate, how many boxes of spaghetti in 1 minute?
  1. At this rate, how many boxes of spaghetti can it pack in 8 minutes?

2)A unicycle wheel makes 196 revolutions in 7 minutes.

Bar Model / Math Statement
  1. At this rate, how many revolutions does it make in 1 minute?
  1. At this rate, how many revolutions does the unicycle wheel make in 15 minutes?

3)Megan babysits for 5 hours and earns $60.

  1. At this rate, how much does she earn in 1 hour?
  1. At this rate, how much will Megan earn if she babysits for 14 hours?

Part B:Read a table to find the information to solve multi-step rate problems

The table shows the fees at a parking lot.

Ben parked his car there from 9 am to 2 pm on the same day.

How much did he pay for parking?

  • Total number of hours: ______
  • Parking fee for the first hour: ______
  • Parking fee for second hour: ______
  • Parking free for the last three hours: ______
  • Total parking fee: ______

The table shows the charges for renting a bicycle.

Tom rented a bicycle from 10 am to 2 pm on the same day.

How much did he pay for renting the bicycle?

  • Total number of hours: ______
  • Charge for the first hour: ______
  • Charge for each additional 1 hour: ______
  • Charge for the last three hours: ______
  • Total charge: ______

Part C:Solve multi-step word problems involving comparison of unit rates

1)Andy needs new batteries for his video game controller. He is trying to decide between two brands. A package of two Brand A batteries costs $3.20. The manufacturer claims the batteries will last for 20 hours. A package of two Brand B batteries cost $2.80. The manufacturer claims the batteries will last for 14 hours. Which battery should Andy buy?

Brand A / Brand B

2)Chloe scored 87 points in 5 basketball games, and Fiona scored 45 points in 2 basketball games. Which of the two players scored more points per game?

Chloe / Fiona

Part D:Find the distance given the speed and time

Mathematical Procedure:

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1)Mr. Anthony drives his truck at a speed of 45 kilometers per hour.

  1. At this speed how far does he travel in 2 hours?
  1. At this speed, how far does he travel in 5 hours?

2)A racing car can travel at a speed of 175 kilometers her hour. How far can the racing car travel in 3 hours?

3)A high-speed train can travel at a speed of 65 meters per second. How far can the train travel in 2 seconds?

Part E:Find the time given the distance and speed

1)Lucas ran around a field at aspeed of 8 meters per second. How long did he take to run a distance of 96 meters?

2)The distance between City X and City Y is 216 kilometers. Mr. Thomas rides his motorcycle at a speed of 54 kilometers per hour. How long does he take to travel from City X and City Y?

Part F:Find the average speed to solve real-world problems

Mathematical Procedure:

Page 175

1)Post A and Post B are 9 meters apart. Post B and Post C are 21 meters apart. A bicycle travels from post A to post B in 2 seconds. Then it travels from Post B to Post C in 3 seconds. Find the average speed of the bicycle for the distance from Post A to Post C.

Average Speed:

2)The distance between Town P and Town Q is 80 miles and the distance between Town Q and Town R is 320 miles. A van takes 2 ½ hours to travel from Town P to Town Q. It takes another 5 hours to travel from Town Q to Town R. Find the average speed of the van for the whole journey.

Average Speed:

3)Celia ran around a 400-meter track two times. It took her 4 minutes to run around the track once and 6 minutes to run around it again. Find Celia’s average speed.

Average Speed: