How many fewer minutes does it take to drive 35 miles at 30 mph than to drive the same distance at 25 mph

To drive 35 miles at 30 mph takes (35/30) hour.
To drive 35 miles at 25 mph takes (35/25) hour.

The difference is  (35/25) minus (35/30).

In order to add or subtract fractions, they need a common denominator.
The smallest one available for this situation is 150 .

(35/25) = 210/150
(35/30) = 175/150

Now we can subtract:    (210/150) - (175/150) = 35/150 of an hour.
(35/150  hour) x (60 min/hr) = (35 x 60) / (150) min = 14 minutes.

==>  It's beginning to look like the answer is NOT 40minutes.
Let's do it again, with a less-elegant but more-intuitive approach:

Time to drive 35 miles at 30 mph = 35/30 = 1-1/6 hours = 70 minutes.
Time to drive 35 miles at 25 mph = 35/25 = 1.4 hours = 84 minutes.

Time saved by driving at 30 mph instead of 25 mph = (84 - 70) = 14 minutes.