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Distance = Rate * Time

Our SAT ACT Math Prep software program contains over 35 topic areas. One of them is Distance = Rate * Time, and this page summarizes the main ideas of this topic. This page is intended for review, and is not a substitute for the interactive, self-paced tutorials of the MathTutor SAT ACT Math prep program.

General Explanation

The formula D = R * T is used in many problems in mathematics. It stands for Distance = Rate * Time. Problems of this type can be solved by using the following steps:
 
  1. Write down the value of all relevant distances, rates, and times. If the value is given, write down its value. If it is unknown, assign a variable name to it.
  2. Write down all D = R * T formulas.
  3. Write down all other formulas.
  4. Solve the resulting equations using standard algebra techniques.

Steps 2 through 4 can often be simplified by limiting yourself to as few variables as possible in Step 1. For example, if two planes travel for the same amount of time, use the same variable name for both. If plane B travels for 2 more hours than plane A, then use t for the time for plane A and t + 2 for the time for plane B.
 
Sometimes it is also helpful to draw a picture
 
Sample Problem

Plane A travels from point A due east at 590 MPH.
Plane B leaves from point B, which is east of A, due west.
 
After two hours, the planes will be 10,180 miles apart. How fast is plane B traveling? Note: the planes are 12,000 miles apart at the start.

Solution

  1. First we need to write down all our variables, distances, etc. 
    2 hrs = time for plane A
2 hrs = time for plane B
590 MPH = rate for plane A
rB = rate for plane B
dA = distance for plane A
dB = distance for plane B
12,000 = initial separation
10,180 = final separation
  2. We write two D = R * T equations, one for each plane. 
    dA = 2 hrs. * 590 MPH = 1,180 miles
dB = 2 hrs. * rB = 2rB
  3. We can deduce by drawing a picture that: 
    12,000 = 1180 + dA + dB
  4. Substituting 1,180 in for dA in the last equation, we get: 
    12,000 = 1,180 + 10,180 + dB
dB = 640
        Substituting dB = 640 into dB = 2rB, we find: 
    640 = 2 * rB
rB = 320

Our final answer is: Plane B is traveling at 320 MPH.

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