# Word Problems Involving Comparing Rates

Rates are one type of ratio.

Rates are utilized to measure the variety of one thing or quantity in comparison to other.

Word problems involving comparing rates deal with distances, time, rates, and wind or water current.

Another type of word problem of equations involved money and age word problems.

## Step-by-step guide to solving comparing rates word problems

- Understand the problem: Read the problem carefully and make sure you understand what is being asked. Identify the key information such as the rates, the time, and the units of measurement.
- Write the rates as fractions: Express each rate as a fraction. For example, if the problem says “a car travels 60 miles in 2 hours,” the rate is 60/2 = 30 miles per hour (mph).
- Compare the rates: Compare the fractions to see which one is larger or smaller. The larger fraction represents the faster rate.
- Use cross-multiplication to find the equivalent rates: In some problems, you may need to find equivalent rates in order to compare them. For example, if one rate is given in miles per hour and the other is given in kilometers per hour, you will need to convert one of them to the other unit. To do this, use cross-multiplication. For example, if the problem says “a car travels 60 miles in 2 hours, and another car travels 100 kilometers in 4 hours,” the equivalent rate is 60/2 = 30 mph and (100*1000)/4 = 25000/4 = 6250 km/h.
- Use the information to answer the question: Once you have identified the key information, use it to answer the question or solve the problem. For example, if the problem asks which car is faster, you would say the first car is faster because it has a faster rate.
- Check your answer: Make sure your answer is reasonable and make sure you have used the correct units of measurement.

**Word Problems Involving Comparing Rates – Examples 1**

Which is the best value?

8 pencils that cost $10 or 5 pencils that cost $8.50.**Solution:**Compare the unit price.

\(\frac{10}{8}=1.25\)

\(\frac{8.50}{5}=0.17\)

5 pencils that cost $8.50 is the best value.

**Word Problems Involving Comparing Rates – Examples 2**

Lucas studies 12 pages of his book in 1 hour. His friend, Mike, studies 5 pages in half an hour. Do Lucas and Mike study at the same rate?**Solution:**Compare studied pages per unit of time.

\(\frac{12}{1}=12\)

\(\frac{5}{0.5}=10\)

So, Lucas studies more pages per unit of time.

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