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?
we can write 2 equations 40 mph is d/40 and 55 mph is d/55 since we saved 25 min we can write d/40-d/55=5/12 the lcm of 40 and 55 is 440
so we have 11d/440-8d/440=5/12
3d/440=5/12
36d=2200
18d=1100
9d=550
d=550/9 miles
which is around 61.1 miles
+414 
