I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

Rate * Time = Distance

Let T be the normal time in hours

25 minutes = 25/60 = 5/12 hr

Equate distances

40 T = 55 ( T - 5/12)

40T = 55T - 275 / 12

275 / 12 = 55T - 40T

275 / 12 = 15 T

275 / [ 12 * 15 ] = T

55/36 hrs = T

D = 40 (55 / 36) ≈ 61.1 miles