In FSX's Learning Center, PP, Lesson 4 (Taught by Rod Machado), how does Rod calculate the figures, "24" and "48" seconds in the Downwind Leg section?

Question

So in Microsoft Flight Simulator X: Steam Edition / Boxed Version, the Learning Center incorporates a section for Flight Lessons, taught by Rod Machado. In Lesson 4: The Traffic Pattern, (in the Private Pilot category) under The Downwind Leg heading, Paragraph 3, Rod states the following:

At 60 knots ground speed, the airplane covers one nautical mile in one minute. Therefore, you'd want to begin the downwind turn anywhere between 30 and 60 seconds after turning crosswind. Since your airplane is climbing at 75 knots (75 knots ground speed assumed), you'll want to begin the turn sooner, perhaps between 24 and 48 seconds after turning crosswind.

How are the values "24" and "48" calculated here? I'm having trouble understanding the mathematical relationship between the 60 knots ground speed covering one nautical mile and the addition of time. (60 knots covering one nm in one minute) He doesn't explain how he gets these values and as such I'm struggling to understand the mathematical formula he's using here.

Answer 1

This is very simple math:

The ratio of times is the same as the ratio of the speeds. You can try calculating this yourself first, and check below for one way to do it:

So the speeds are 60kts and 75 kts, and the times are 30s to 60 s and 24s to 48s.

Find ratio of speeds:

60/75=0.8

Apply the ratio to times:

30x0.8=24 and 60x0.8=48

The faster you go the more ground you cover in a unit of time. Hence less time is needed to cover same distance.