## Distance = Rate * Time
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:
- 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.
- Write down all D = R * T formulas.
- Write down all other formulas.
- 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
- 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 r _{B}= rate for plane B d_{A}= distance for plane A d_{B}= distance for plane B 12,000 = initial separation 10,180 = final separation - We write two D = R * T equations, one for each plane.
d _{A}= 2 hrs. * 590 MPH = 1,180 miles d_{B}= 2 hrs. * r_{B}= 2r_{B} - We can deduce by drawing a picture that:
12,000 = 1180 + d _{A}+ d_{B} - Substituting 1,180 in for d
_{A}in the last equation, we get:12,000 = 1,180 + 10,180 + d Substituting d_{B}d_{B}= 640_{B}= 640 into d_{B}= 2r_{B}, we find:640 = 2 * r _{B}r_{B}= 320
Our final answer is: Plane B is traveling at 320 MPH. |