When working on Distance-Rate-Time questions, you will inevitably use one of the following three formulas.

1. Distance = (Rate)(Time)

2. Rate = Distance/Time

3. Time = Distance/Rate

Did you know that there’s a quick and easy shortcut for recalling all three formulas?

The shortcut is similar to some of the shortcuts you learned in highschool science. It looks like this: D/RT (aka, the “DiRT” shortcut). As you may have guessed, D = distance, R = rate, and T = time.

Can you see all three formulas hiding in the simple fraction D/RT?

Here’s how it works. Let’s say, you need to recall the formula for finding the time it takes to complete a certain trip. Simply take the fraction D/RT and remove the T (for time). This leaves you with D/R. In other words, Time = Distance/Rate.

Similarly, if you need to recall the formula for finding the rate (speed), simply take the fraction D/RT and remove the R (for rate). This leaves you with D/T. In other words, Rate = Distance/Time.

Finally, if you need to recall the formula for finding the distance, take the fraction D/RT and remove the D (for distance). This leaves you with RT. In other words, Distance = (Rate)(Time).

So, instead of memorizing 3 formulas, just remember DiRT, which stands for D/RT.

In general, the distance formula is used to determine the distance between two points on a coordinate plane. The formula is useful for questions a variety of coordinate geometry questions. For example, you can use the distance formula to calculate the length of a side of a triangle or rectangle on the coordinate plane.

Hey Chris,
Thanks for great article I have a question though.
Could you expand your idea concerning Distance, Rate, Time and expound upon a little different situation when two cars/trains/bicycles etc.
1. move towards each other from opposite directions..
2. move from one point to different directions (left -right)..
Any shortcuts here, sometimes these kinds of problems could be really tough to tackle in 2 minutes
Thank you for your hard work!
Eraj

I think you meant 1) If two things are moving towards each other from opposite directions, find the difference or calculate the difference in their respective rates.
For example, based on this link and example you used, you had subtracted the speed of the slower train from the speed of the faster train. https://magoosh.com/gre/2011/how-a-moving-train-can-be-stationary/

Sorry, I see what you meant in your previous post. You meant if two things are moving in the same direction, then calculate the difference as you can think of the problem in a manner whereby one of the things is stationary.

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hey Chris

I just had a look at the MAGOOSH GRE E-BOOK. I was wondering to what type of problem you were referring with the distance formula?

Thanks,

Hi Yasmine 🙂

In general, the distance formula is used to determine the distance between two points on a coordinate plane. The formula is useful for questions a variety of coordinate geometry questions. For example, you can use the distance formula to calculate the length of a side of a triangle or rectangle on the coordinate plane.

I hope this helps a little 🙂

Hey Chris,

Thanks for great article I have a question though.

Could you expand your idea concerning Distance, Rate, Time and expound upon a little different situation when two cars/trains/bicycles etc.

1. move towards each other from opposite directions..

2. move from one point to different directions (left -right)..

Any shortcuts here, sometimes these kinds of problems could be really tough to tackle in 2 minutes

Thank you for your hard work!

Eraj

Hi Eraj,

Good question :). To elaborate:

1) When two things are moving towards each other from opposite directions, add their respective rates.

2) When two things are heading in opposite directions from a fixed point, add their respective rates.

Hope that helps!

Hey Chris,

I think you meant 1) If two things are moving towards each other from opposite directions, find the difference or calculate the difference in their respective rates.

For example, based on this link and example you used, you had subtracted the speed of the slower train from the speed of the faster train.

https://magoosh.com/gre/2011/how-a-moving-train-can-be-stationary/

Thanks,

Samy

Sorry, I see what you meant in your previous post. You meant if two things are moving in the same direction, then calculate the difference as you can think of the problem in a manner whereby one of the things is stationary.

Sorry for the confusion and thanks Chris.