There are several ways this can be done, some easier than others. Some methods require nothing more than pencil and paper, while some demand specialised equipment and the latest speed tables. You will, of course, need a means of measuring distance.
In order to compute time, speed and distance problems we have to know time and we have to know distance. To tell time we need an instrument that will perform consistently in the face of vibration and the bouncing of a car on rally roads. IT MUST BE AN INSTRUMENT THAT IS EASY AND FAST TO READ. Stopwatches easily meet these qualifications. They are readily available and relatively inexpensive.
A decimal readout or dial watch THAT READS IN HUNDREDTHS OF A MINUTE INSTEAD OF SECONDS (that is, 1/60th of a minute), although more expensive and difficult to find, SIMPLIFIES CALCULATIONS NO END. Trying to add or to or subtract from minutes and seconds involves (for example) converting 13 minutes 24 seconds into 12 minutes 84 seconds if you have to subtract any quantity with more than 24 seconds from it. The decimal readout or dial, on the other hand, gives us 100 parts to the minute, and arithmetic becomes a simple as counting.
For checking out or zeroing in your watches and clocks for exactly the correct time of day, DO NOT RELY UPON THE RADIO TIME ANNOUNCEMENTS. They are quite often incorrect. Instead, check your timing equipment with the rally Official.
Rally Officials will be timing and scoring your car with stopwatches that read in hours: minutes: seconds: hundredths of seconds. Arriving early or late at a checkpoint adds penalty points to your score at a rate determined by the Rally Officials. (A typical penalty would be 1 point for each second you are early or late.) The team with the least number of penalty points wins the rally. | 
No rally is going to be that simple. There will be average speeds of 24.37 mph, or 31.24 mph or anyone of thousands selected by the Rally Officials. Obviously you will need a table for each average speed. If your friendly rally Official he might even include basic tables in his General Instructions. You should obtain a set of your own tables if you plan to run rallies regularly. Average Speed Tables, first published in 1959, is an old standby. Try to get a newer set in decimal minutes. Older versions gave time in seconds, but are still useful. Another type of table is Cone's Factors, which not only gives you minutes per mile at an indicated average speed, but also takes into account odometer error. Some of these materials are still readily available today. Try your local library, other rallyists, or the classified section of automotive magazines. 
Not all navigators like to work with tables. Some like to work with circular rally indicators like the Stevens Model 25 or the Blackwell Rally Indicators which have scales for time, speed and distance. 
Using movable pointers, these indicators show graphically the time and distance combinations for an infinite number of average speeds. Some even have the added refinement of accommodating odometer error. Other methods utilise slide rules, pocket calculators or computers, onboard original equipment tripcomputers, and even the old mechanical Curta "pepper mill" calculator that works by turning a crank. It is expensive and difficult to find as it is no longer manufactured, but has been the favourite of serious rallyists for many years. The Curta was manufactured in Liechtenstein. RAC Rally rules permit all of the aforementioned devices except for portable or aftermarket electronic computers and aftermarket electronic, electro-mechanical. NONE OF THESE DEVICES WILL THINK FOR YOU & THEY WON'T KEEP YOU FROM GETTING LOST!