The time difference between driving at 60 mph and 40 mph is 45 minutes, which is 3/4 of an hour. So, the equation for the time you spent driving is:
time = (rate * time_difference) / (rate - new_rate)
Plugging in the known values, we get:
time = (40 mph * 3/4 hours) / (40 mph - 25 mph)
time = 7.5 hours
Since the rate is in miles per hour and the time is in hours, the distance traveled is simply the product of the two:
distance = rate * time
distance = 40 mph * 7.5 hours
distance = 300 miles
Therefore, you drove 300 miles to the beach.
