I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 50 miles per hour instead, then I would have arrived 25 minutes earlier. How many miles did I drive?

maximum Aug 4, 2023

#1**+1 **

Call the time in minutes driving 40 mph = M

Using Distance / Rate = Time...... we have in the first case

D / 40 = M (1)

In the second case we must convert 25 min to hrs = 25/60hrs = 5/12 hrs....so we have that

D / 50 = M - 5/12 (2)

Sub (1) into (2)

D /50 = D/40 - 5/12 rearrange as

D/40 - D/50 = 5/12

5D / 200 - 4D /200 = 5/12

D / 200 = 5/12

D = 200 * 5/12 = 1000/12 = 250 / 3 miles = 83 1/3 miles

CPhill Aug 4, 2023