On a roundtrip by car, it took 2 hours longer on the return trip than it did on the first leg of the trip. How much faster did the car go on the first part of the trip?

Question

On a roundtrip by car, it took 2 hours longer on the return trip than it did on the first leg of the trip.  How much faster did the car go on the first part of the trip?

lukebluefive · Answer

Remember that:
$$Speed = \frac{Distance} {Time}$$
So, since the trip there and back is the same distance, by rewriting the equation in the following way:
$$Distance = Speed \times Time$$
And equating the two legs of the trip:
$$Speed_1 \times Time_1 = Speed_2 \times Time_2$$
We are given the following equation:
$$Time_2 = Time_1 + 2$$
Substituting this into the previous equation gives:
$$Speed_1 \times Time_1 = Speed_2 \times (Time_1 + 2)$$
Multiplying out:
$$Speed_1 \times Time_1 = Speed_2 \times Time_1 + 2 \times Speed_2$$
Divide both sides by the first time to get your equation.