Question

I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 35 miles per hour instead, then I would have arrived 45 minutes later. How many miles did I drive?

Answer 1

Let's call the distance you drove "d" and the time it took you to drive that distance at 40 mph "t".

Using the formula distance = rate × time:

d = 40t

We also know that if you had driven at 35 mph instead, you would have arrived 45 minutes (or 0.75 hours) later. So the time it would have taken you to drive that same distance "d" at 35 mph would be:

t + 0.75

Using the formula again, but this time with a rate of 35:

d = 35(t + 0.75)

Now we have two equations for "d", which we can set equal to each other:

40t = 35(t + 0.75)

40t = 35t + 26.25

5t = 26.25

t = 5.25

So it took you 5.25 hours to drive to the beach at 40 mph.

Now we can use either of the two equations we set up earlier to find "d". Let's use the first one:

d = 40t

d = 40(5.25)

d = 210

So you drove 210 miles to get to the beach.