Step-by-step Guide on How to Use Unit Rates to Solve Word Problems
Read,3 minutes
1. Read the Problem Carefully: Start by reading the word problem thoroughly. Understand the scenario being presented and identify what the problem is asking for. Is it asking for the total cost, total time, total distance, or some other total quantity? You need to know this to determine what you are solving for.
2. Identify the Rates: Next, identify the rates presented in the problem. For instance, you might be given a speed (like miles per hour), a cost (like dollars per pound), or some other type of rate.
3. Find the Unit Rate: The unit rate is simply the rate for one unit of a given quantity. To find it, you'll typically divide the total quantity by the total number of units. This tells you, for instance, how much one pound of apples costs, how far you can travel in one hour, or how much you can earn in one hour of work.
4. Set Up the Equation: Now that you have the unit rate, you can set up an equation to solve the problem. This usually involves multiplying the unit rate by the number of units involved in your specific scenario.
5. Solve the Equation: Finally, solve the equation to find the answer to the problem. Be sure to check your answer to ensure it makes sense in the context of the problem.
6. Verify Your Answer: Always verify your solution. Does the solution make sense in the context of the problem? If not, you might need to revise your calculations.
Example
Suppose you're driving to a city that's 300 miles away. Your car can travel at a speed of 60 miles per hour. How long will it take to get there?
1. Read the Problem: We want to know how long the trip will take.
2. Identify the Rates: We know the car travels at 60 miles per hour.
3. Find the Unit Rate: Here, the unit rate is already given: 60 miles per hour.
4. Set Up the Equation: We need to find the total time, so we'll divide the total distance by the speed: \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \).
5. Solve the Equation: \( \text{Time} = \frac{300 \text{ miles}}{60 \text{ miles per hour}} = 5 \text{ hours} \).
6. Verify Your Answer: It makes sense that it would take 5 hours to travel 300 miles at a speed of 60 miles per hour.
And there you have it! We've used the unit rate to solve a word problem. Practice this method with other word problems to become more comfortable with it.
