Final answer:
To solve this problem, we need to set up an equation using the average speed formula and the given information. We can then solve the equation to find the values of x and d.
Step-by-step explanation:
Let's say Shane's rate of travel to his destination is x mph, and his rate of travel back home is x + 7 mph.
The formula for finding average speed is total distance divided by total time. Let's assume the distance to his destination is d miles.
His travel time to his destination is d divided by x, and his travel time back home is d divided by x + 7.
Since his whole travel time is 11.4 hours, we can write the equation:
d/x + d/x + 7 = 11.4
To solve for d, we need to use the fact that the total distance for the round trip is 160 miles in each direction.
Therefore, we have the equation:
160/x + 160/x + 7 = 11.4
Solving this equation will give us the values of x and d to find Shane's rates of travel and the distance to his destination respectively.