+2651 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?
+106 Let's use the "distance = rate (or speed) times time". Let's suppose that d represents the distance to the beach and t represents the time taken to drive to the beach at 40 mph.Then we can represent what we said as these equations:
\(d = 40 \times t\)
\(d = 55 \times (t - 5/12)\)
We can now simplify these equations and solve for d like this:
\(d = 55t - 275/12\)
\(55t - 275/12= 40t\)
\(15t= 275/12\)
\(t = 55/36\)
\(d = 55/36 \times 40\)
\(d = 550/9\)
So the distance you will drive will be 550/9 miles.
