Sometimes we are given an equation with multiple variables, as in multiple letters. Most of these variables will be known, so we can replace the variables in our equation with the numbers that we know they are equal to. Once we’ve replaced these variables with numbers, we can solve for whichever variable is left. The following video will show you how to do this with a few examples.

Substitute Values into an Equation and Solve for a Variable

Video Source (07:40 mins) | Transcript

Once we substitute the values we know into the equation, solving the equation is just the same as what we’ve learned in the previous lessons.

## Additional Resources

- Khan Academy: Finding Average Speed or Rate (13:14 mins, Transcript)

### Practice Problems

- A train traveled for \(t=5\) hours at a constant speed of \(r=60\) miles per hour. Use the formula \(d=r \cdot t\) to find the total distance (\(d\)) the train traveled (in miles). (Solution
- A man walked a distance of \(d=15km\) (kilometers) in \(t=3\) hours at a constant rate. Use the formula \(d=r \cdot t\) to find the speed (\(r\)) of the man in km per hour. (Solution
- A boat traveled a distance of \(d=140\) miles at a constant speed of \(r=70\) miles per hour. Use the formula \(d=r \cdot t\) to find the number of hours (\(t\)) that the trip took. (Solution
- A bus traveled for \(t=3.1\) hours at a constant speed of \(r=62\) miles per hour. Use the formula \(d=r \cdot t\) to find the total distance (\(d\)) the bus traveled (in miles). Round your answer to the nearest tenth. (Video Solution
- A truck traveled a distance of \(d=615km\) (kilometers) over \(t=5.9\) hours at a constant rate. Use the formula \(d=r \cdot t\) to find the speed (\(r\)) of the truck in km per hour. Round your answer to the nearest tenth. (Solution
- A bicyclist traveled a distance of \(d=18.6\) miles at a constant speed of \(r=16\) miles per hour. Use the formula \(d=r \cdot t\) to find the number of hours (\(t\)) that the trip took. Round your answer to the nearest tenth. (Video Solution

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