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If a person travels for 3 hours at 50 miles per hour, we can find the total distance traveled by multiplying:

/*times*
= 150miles

This is similar to ##converting between units#{math/measurments}#); here, miles per hour is treated as a conversion factor, since 50 miles is equivalent to 1 hour, in a sense.

In general, to find the total distance traveled, multiply the total time spent traveling by the rate of travel. This can be expressed as an equation:

Using this equation, we can writed=rtwhered= total distance,r= rate of travel, andt= time

r= andt=

*Example 1*: If Sue drives 45 minutes at 80 miles per hour, how far does she travel?

45 minutes =
hour

*d* = *rt* = ×hour = 60miles

*Example 2*: If Sue drives 200 miles at 80 miles per hour, how long does it take her?

*t* = = = 200miles× = 2.5hours

*Example 3*: If Sue drives 200 miles in 4 hours at a steady pace, how fast is she traveling?

*r* = = = 50miles per hour

**Hint:** Make sure the units in your calculation cancel out to yield the units your answer should be in. If they don't, you've probably used the wrong units in your calculation or the wrong equation. Be careful, however, since units are not variables or numerical quantities, and multiplying or canceling them is only a way to check your work.

Occasionally, we will run into a problem involving two "travelers."

For example:

Bonnie and Barbara are driving from Point A to Point B. Barbara arrives at Point B in 2 hours. Bonnie travels 15 miles per hour faster than Barbara, and arrives at Point B in 1.5 hours. How fast does each woman travel?

To solve a problem involving two travelers, follow these steps:

- Figure out which quantity related to the travelers is equal (a time, distance, or rate).
- Write two expressions for that quantity, one using each "traveler."
- Set the two expressions equal to each other and solve the equation.

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