All the units in your RTD chart must match up with one another. The two units in the rate should match up with the unit of time and the unit of distance. For example:
It takes an elevator four seconds to go up one floor. How many floors will the elevator rise in two minutes?
The rate is 1 floor/4 seconds, which simplifies to 0.25 floors/second. Note: The rate is NOT 4 seconds per floor! This is an extremely frequent error. Always express rates as “distance over time,” not as “time over distance.”
The time is 2 minutes. The distance is unknown.
Watch out! There is a problem with this RTD chart. The rate is expressed in floors per second, but the time is expressed in minutes. This will yield an incorrect answer.
| R (floors/sec) |
× | T (min) |
= | W (floors) |
|
| Elevator | 0.25 | × | 2 | = | ? |
To correct this table, change the time into seconds. Then all the units will match. To convert minutes to seconds, multiply 2 minutes by 60 seconds per minute, yielding 120 seconds.
| R (floors/sec) |
× | T (sec) |
= | D (floors) |
|
| Elevator | 0.25 | × | 120 | = | ? |
Once the time has been converted from 2 minutes to 120 seconds, the time unit will match the rate unit, and you can solve for the distance using the RT = D equation:
| 0.25(120) = d | d = 30 floors |
Another example:
A train travels 90 kilometers/hour. How many hours does it take the train to travel 450,000 meters? (1 kilometer = 1,000 meters)
First, divide 450,000 meters by 1,000 to convert this distance to 450 km. By doing so, you match the distance unit (kilometers) with the rate unit (kilometers per hour).
| R (km/hr) |
× | T (hr) |
= | D (km) |
|
| Train | 90 | × | t | = | 450 |
You can now solve for the time: 90t = 450. Thus, t is 5 hours. Note that this time is the “stopwatch” time: if you started a stopwatch at the start of the trip, what would the stopwatch read at the end of the trip? This is not what a clock on the wall would read, but if you take the difference of the start and end clock times (say, 1pm and 6pm), you will get the stopwatch time of 5 hours.
The RTD chart may seem like overkill for relatively simple problems such as these. In fact, for such problems, you can simply set up the equation RT = D or RT = W and then substitute. However, the RTD chart comes into its own when you have more complicated scenarios that contain more than one RTD relationship, as you’ll see in the next section.
Convert 10 meters per second to meters per hour.
It takes an inlet pipe 2 minutes to supply 30 gallons of water to a pool. How many hours will it take to fill a 27,000 gallon pool that starts out empty?