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?

ChiIIBill Jun 18, 2024

#1**0 **

Lets assume d as the distance from the origin to the beach. Then, by the d=rt formula, it would have taken d/40 hours to get to the beach. If the speed was increased to 55mph, it would have taken d/55 hours. We are given this value is 25 minutes (or 5/12 hours) smaller than d/40. We can now set up the equation \(\frac{d}{55}+\frac{5}{12}=\frac{d}{40}\) and multiply the gcd of 55, 12, and 40 to both sides. The gcd happens to be 1320, so the equation turns into \(24d+110=33d\). Therefore, d=110/9 (notice how I got too lazy to use latex).

I may have made a mistake here, so feel free to tell me if I did. :D

Tottenham10 Jun 19, 2024