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News from Mathnasium of Richmond BC

Word Problem of the Week: Units and Unit Rates

Jul 8, 2020

 

Introduction

Unit rates are used in all sorts of everyday applications. Maybe you’ve used kilometres per litre to estimate the next time you’ve needed to get gas, or used unit prices at the store to decide whether or not to buy in bulk. This week’s word problems will give your child practice with units and unit rates and help familiarize them more with this important math concept.

Choose the word problem that’s the right skill level your child, and have them give it a try! After they feel they’ve found the answer, scroll down for the solution!

They Really Come in Handy!

You may think you’ve never heard of a unit rate, but you use them all the time! A unit rate measures the number of something per 1 unit of something else. For example, 50 kilometres per hour, four students per teacher, and so on. Let’s practice using units and unit rates to solve this week’s word problems.

Pick the word problem below that’s the right skill level for you. Take your time working it out. When you feel you’ve found the answer, scroll down below to check your solution against ours. No peeking, and have fun!

Lower Elementary:
Question: Anthony sails 14,500 kilometres from Turkey to Peru. If Anthony takes the same route back to Turkey from Peru, how far will he have sailed in total?

Upper Elementary:
Question: Nellie puts a batch of pies into the oven at 6:17 AM. When they go into the oven, the internal temperature of the pies is 60° Fahrenheit. The temperature increases at a rate of 2.5° per minute. If Nellie wants the internal temperature of the pies to reach 160°, at what time should she take them out of the oven?

Middle School:

Question: It takes a barber 12 minutes to shave a face and 30 minutes to give a haircut. The barber works for 3 hours straight and spends twice as much time shaving faces as he does giving haircuts. If none of his customers get both a haircut and a shave, then how many customers does he see in total?

Algebra and Up:
Question: A cottage by the sea has a value of $750,000, which has increased at an annual rate of 5% for the past 10 years. How much was the cottage worth 10 years ago? You may use your calculator.

Solutions

Great job on today’s word problem! Are you ready to check your answer? Look below to see if your solution matches ours.

Lower Elementary:
Answer: 29,000 kilometres 
Solution: Anthony’s route from Turkey to Peru and back again is 14,500 + 14,500 = 29,000 kilometres in total. Remember to carry the 1 in the thousands place!

Upper Elementary:
Answer: 6:57 AM
Solution: In order to increase to 160°, the internal temperature of the pies will need to rise 160° – 60° = 100°. Since 100° ÷ 2.5° per minute = 40 minutes, it’ll take 40 minutes for the pies to bake. So, Nellie should take them out of the oven at 6:57 AM.

Middle School:
Answer: 12 customers
Solution: If the barber spends twice as much time shaving faces as he does giving haircuts, he must spend 2 hours shaving faces and 1 hour giving haircuts. Since it takes 12 minutes to shave a face, the barber shaves 5 faces per hour–that’s 10 in 2 hours. Each haircut takes 30 minutes, so he can give 2 haircuts in an hour. That means he sees 10 + 2 = 12 customers.

Algebra and Up:
Answer: $460,434.94
Solution: The value of the cottage is currently $750,000, and it was worth C dollars 10 years ago. If its value has increased 5% each year for the past 10 years, then we know that $750,000 = C × 1.0510. To solve for C, we divide $750,000 ÷ 1.0510 = $460,434.9402, which rounds to $460,434.94.