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In the Trans-Yukon Rally Race, which is currently underway, they give a four minute window between start times for each team to space the vehicles out on the course. Each team's finish in the race is then determined by their individual time to complete the course. There are five teams that are sponsored by American motor companies. The drivers of the American teams, their current mileage into the race, and their official times at that point of the race are listed in the table below.

Name Mileage Time
(hours:minutes:seconds)
Adam 1:49:48
Allen 1:36:00
Nigel 0:51:00
Owen 1:12:00
William 1:27:00

Which sets of drivers are progressing at the same pace?

Adam and William
Owen and William
Adam and Allen
Allen and Owen
Nigel and William
Nigel and Owen

1 answer

To determine which sets of drivers are progressing at the same pace, we can calculate the average speed of each driver based on their mileage and time, then compare these speeds.

First, let's convert the time for each driver into total seconds for easier calculations.

  1. Adam: 1:49:48 = (1 * 3600) + (49 * 60) + 48 = 6588 seconds
  2. Allen: 1:36:00 = (1 * 3600) + (36 * 60) + 0 = 5760 seconds
  3. Nigel: 0:51:00 = (0 * 3600) + (51 * 60) + 0 = 3060 seconds
  4. Owen: 1:12:00 = (1 * 3600) + (12 * 60) + 0 = 4320 seconds
  5. William: 1:27:00 = (1 * 3600) + (27 * 60) + 0 = 5220 seconds

Next, we compare the mileage and time to calculate the pace (miles per second). However, since we don’t have the mileage for reference, we will focus instead on the time progression by examining relative performance.

Now we can simply compare the times to find if any two drivers have the same time per mile, which would indicate they are progressing at the same pace.

  • Adam: 6588 seconds
  • Allen: 5760 seconds
  • Nigel: 3060 seconds
  • Owen: 4320 seconds
  • William: 5220 seconds

Now figuring out their relative rates:

We will need the relationship (time/speed) and if two drivers have the same (time/mileage) ratio, they are effectively on the same momentum/given the missing mileage data we can still state as follows for equal progress:

  • Given that Adam (6588 seconds) and William (5220 seconds) have different times, they are not at the same pace.
  • Owen (4320 seconds) has a different time as well.
  • Allen (5760 seconds) shows a distinct timing between all.
  • Nigel (3060 seconds) shows a distinct time as well.

Considering all the data and the fact the times do not repeat implies:

We will identify that the only two that show marked differences are:

  • Owen and William : Different paces.
  • Allen and Owen: Different paces.
  • Adam and Nigel: Different paces in total counts.
  • Adam and Allen are too various.

Hence, through this analytic review, all drivers have some level of differing progress through the pace conclusion and show variance distinctly making for all teams progressing at different speeds. No sets of drivers are progressing at the same pace.

Thus, No pairs match for the same pace in clear terms.