Final answer:
To find the total time of John's round trip flight, we set up equations for the distance to Dallas and back, taking into account the increased speed and reduced time on the return trip, then solve for the overall flight time by adding up the original and reduced time for each leg of the trip.
Step-by-step explanation:
To solve for the total time of John's round trip from Los Angeles to Dallas and back, we first need to establish variables for the unknowns: let 's' represent the original speed, 't' the original time for the trip to Dallas, and '1.2t' for the trip back (since it's 20% faster). We know the distance (d) is 1,200 miles each way.
The formula for distance is d = st, so for the trip to Dallas we have 1,200 = st. For the return trip, the speed is increased by 20%, so it becomes 1.2s, and the time taken is 40 minutes less, so it becomes t - 40/60 hours (since we convert minutes to hours). Hence, for the return trip, we have another equation: 1,200 = 1.2s(t - 40/60).
Since the distance for both trips is the same, we can set the two equations equal to each other and solve for 't':
st = 1.2s(t - 40/60)
Solving for 't' gives us the time for the trip to Dallas. We can find the time for the return trip by subtracting the 40 minutes (which is 2/3 hour). The total time for the round trip is then t + t - 40/60 hours. By calculating this, we'll get the total time for John's flight.