Question

I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 30 miles per hour instead, then I would have arrived 20 minutes later. How many miles did I drive?

Answer 1

Answer:

40

Step-by-step explanation:

Let $d$ be the distance to the beach, in miles. Then the time it took to drive to the beach, at 40 miles per hour, is $d/40$ (in hours).

If I had driven at 30 miles per hour instead, then it would take me $d/30$ hours. Note that 1 hour is equivalent to 60 minutes, so 20 minutes is equivalent to $20/60 = 1/3$ of an hour. Therefore,

\[\frac{d}{40} = \frac{d}{30} - \frac{1}{3}.\]Multiplying both sides by 120 to get rid of the fractions, we get

\[3d = 4d - 40,\]so $d = \boxed{40}$.

Answer 2

Answer:

40 miles

Step-by-step explanation:

Let's set x to the number of miles driven, and t to the number of hours it took to drive.

We know that 40t is equal to x.

We also know that 40t is equal to 30(t + 1/3).

Solve for t:

40t = 30(t+1/3)

40t = 30t + 10

Subtract 30t from both sides:

10t = 10

Divide 10 from both sides:

t = 1

40t = 40 x 1 = 40 miles