What does it mean that an overall time is less than 100 minutes?
B
How can we estimate the time it takes us to run 3.1 miles?
A
More than 0 and less than 36.4 minutes.
B
See solution.
Practice makes perfect
We take part in a triathlon and we already completed 2 events. Our goal is to finish an overall time of less than 100 minutes. We will find the time we can take to finish the running event and still meet our goal. To do this, let's see the table that shows our time for 2 first events.
Triathlon
Event
Our Time (minutes)
Swimming
18.2
Biking
45.4
Running
?
Now, finishing the triathlon with an overall time of less than 100 minutes means that the sum of times of all activities is less than 100.
Swimming Time + Biking Time + Running Time is less than 100 minutesThis sentence represents an inequality. The key phrase is is less than. It divides the sentence into what should be on the right-hand side and the left-hand side. We can identify is less than with <.
Swimming Time + Biking Time + Running Time < 100 minutes
From our table, we know Swimming Time and Biking Time. Let's substitute the values into our inequality! These are our constants just like 100.
18.2 + 45.4 + Running Time < 100 minutes
Our variable — the quantity we want to find — is Running Time. Let's call it x.
18.2 + 45.4 + x < 100
Let's solve the inequality to find the possible number of minutes we can take to finish the triathlon in less than 100 minutes.
All values of x less than 36.4 will satisfy the inequality.
x < 36.4
Running time is less than 36.4 minutes.
Note that Rumnning Time represents the time. This is why it cannot be negative.
0 < x < 36.4
This means that the running time can be any number between 0 and 36.4 minutes to meet our goal.
We want to estimate how long it would take us to run 3.1 miles. Suppose we know the time it takes us to run 1 mile. To estimate the time of running 3.1 miles, we can multiply this number by 3.1. Let's assume that we run 1 mile in 10 minutes.
3.1 * 10 = 31 minutesBecause 31 is less than 36.4, we would reach our goal! Next, let's suppose we run 1 mile in 15 minutes and again estimate the time of running 3.1 miles.
3.1 * 15 = 46.5 minutes
With this speed, it would take us 46.5 minutes to run 3.1 miles. Because this is more than 36.4 minutes, our goal would be not achieved. Using the following applet you can enter the time you estimated on your own and check your answer!
