You can virtually guarantee that you are going to see at least one problem involving the distance formula on your SAT. It's a simple formula, but variations on it can get tricky. Today we'll look at how the distance formula is used on the SAT.

Distance Formula

Question:

Malcolm drove 150 miles. He made the trip in 2½ hours with no stops. How fast did he drive?

• You know the distance and the time. Plug them into the distance formula to calculate the rate:

   150 = 2.5r
60 = r

Malcolm drove 60 mph.

Round Trips

A more common (and more difficult) way that you will see the distance formula used on the SAT is in a round trip. The rate and the time will be different coming and going. Bear in mind that in a round trip, if you take the same route coming and going, the distance is the same both ways.

Question:

It took Elena 20 minutes to get to work today driving at an average speed of 45 mph. She drove home by the same route, but traffic was heavy and it took her 30 minutes to get home. How fast did she drive on the way home?

• We know that the distance is the same going to work as it is coming home:

D_{going to work} = D_{coming from work}

• Therefore,

r_going × t_going = r_coming × t_coming

• Now, plug in the values you were given and solve:

45 × 20 = r_coming × 30
       900 = r_coming × 30
  = r_coming

Elena drove 30 mph coming home.

Question:

At cross-country practice, Tyler ran up a hill at 2 mph. He took the same path on the way back down at an average speed of 3 mph. It took him an hour to complete the run. How long did it take him to get up the hill?

• You know the distance up the hill is the same as the distance down the hill, you know the rates going up and down, and you know the total time that the run took. Let's begin to set up a formula:

                       r_up × t_up = r_down × t_down
                   2t_up = 3t_down

• You know that the total time is one hour. So:

t_up + t_down = 1
                  t_down = 1 - t_up

• Substitute 1 - t_up for t_down into the first equation:

                        2t_up = 3(1 - t_up)
                        2t_up = 31 - 3t_up
            5t_up = 3
              t_up =

• It took Tyler (or 0.6) of an hour to get up the hill. That will probably not be one of your answer choices, since we don't customarily give time in fractions of an hour. Convert it to minutes:

× 60 = 36 minutes