Final answer:
An equation that relates the speed on the first leg (y mph) to the speed on the second leg (x mph, with x = y + 20) of a 700-mile roundtrip journey can be expressed as 350/y - 350/(y+20) = 2. Solving this equation algebraically will provide the speeds for both legs of the trip.
Step-by-step explanation:
To construct an equation that relates the speeds of the two legs of the trip, where x represents the speed on the second leg of the trip, we must first understand that the total distance traveled is the sum of the distances for each leg. Since the total roundtrip distance is 700 miles and the trip is there and back, each leg must be 350 miles.
Let the speed on the first leg be y mph and the second leg be x mph, where it is given that x = y + 20. Since speed is distance divided by time, the time for each leg can be represented as 350/y for the first leg and 350/x for the second leg. The problem states that increasing the speed by 20 mph saved 2 hours on the return trip, so the time taken for the first leg minus the time taken for the second leg is 2 hours.
Using this information, we can write the following equation:
350/y - 350/x = 2
Since x = y + 20, we can substitute x with y+20 in our equation to find the relationship between y and x solely in terms of x:
350/y - 350/(y+20) = 2
This is the equation that relates the speeds of the two legs of the trip. Some algebra will be required to solve for x or y.