Justin runs at a constant rate, traveling in hours.Write an equation that shows the relationship between , the distance he runs in kilometers, and , the time he spends running in hours.Do NOT use a mixed number.
Question
Justin runs at a constant rate, traveling in hours.Write an equation that shows the relationship between , the distance he runs in kilometers, and , the time he spends running in hours.Do NOT use a mixed number.
Solution
Let's denote:
- d as the distance Justin runs in kilometers
- t as the time he spends running in hours
Since Justin runs at a constant rate, the relationship between the distance he runs and the time he spends running is a linear one. This means that the distance he runs (d) is directly proportional to the time he spends running (t).
We can express this relationship with the following equation:
d = rt
where:
- r is the rate at which Justin runs.
However, the problem does not provide a specific rate. If we knew Justin's rate, we could substitute it into the equation. For example, if Justin runs at a rate of 5 kilometers per hour, the equation would be:
d = 5t
Without a specific rate, the best we can do is leave r in the equation as a variable. So the equation that shows the relationship between the distance Justin runs and the time he spends running is:
d = rt
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