Question

While traveling to and from a certain destination, you realized increasing your speed by 40 mph saved 4 hours on your return. The total distance of the round trip was 640 miles. Construct an equation that relates the speeds of the two legs of the trip. Use x to represent the speed on the second leg of the trip.

Answer 1

To construct an equation that relates the speeds of the two legs of the trip, let's start by representing the speed on the first leg as y mph. On the first leg of the trip, the time taken is 640/y hours. On the return trip, the speed is increased by 40 mph, making it x+40 mph. The time taken on the return trip is 640/(x+40) hours. According to the given information, increasing the speed by 40 mph on the return trip saved 4 hours. So we can set up the equation: 640/y - 640/(x+40) = 4. Simplifying this equation will give us the relation between the speeds of the two legs of the trip.

Step-by-step explanation:

To construct an equation that relates the speeds of the two legs of the trip, let's start by representing the speed on the first leg as y mph.

On the first leg of the trip, the time taken is 640/y hours.

On the return trip, the speed is increased by 40 mph, making it x+40 mph. The time taken on the return trip is 640/(x+40) hours.

According to the given information, increasing the speed by 40 mph on the return trip saved 4 hours. So we can set up the equation:

640/y - 640/(x+40) = 4

Simplifying this equation will give us the relation between the speeds of the two legs of the trip.