Final answer:
The total time for a round trip was 11 hours, with varying speeds for each direction. By setting up equations representing the travel times for each leg and solving the system of equations using the total time and speeds given, we calculate the time for Logan's return trip to college and express it in hours and minutes.
Step-by-step explanation:
To find out how much time it took Logan to drive from home back to college, we need to use the formula distance = speed x time. Since the distance to the college and back home is the same, let's call that distance d. We don't know d, but we can express the time it took for each leg of the trip in terms of d.
On the trip home from college, Logan's speed was 66.8 mph. So the time it took for the first trip, t1, can be expressed as t1 = d/66.8 hours.
On the trip back to college, Logan's speed was 57.7 mph, which means the time for the second trip, t2, is t2 = d/57.7 hours.
We know the total time for both trips was 11 hours, which can be written as:
t1 + t2 = 11 hours
Substituting the expressions for t1 and t2 we get:
d/66.8 + d/57.7 = 11
To solve this, we combine the terms by finding a common denominator, which is 66.8 x 57.7, and solve for d. After finding the value for d, we then calculate t2 specifically, which is the time Logan took to drive back to college.
Once we have t2 in hours, to express it in minutes we convert the decimal part of the time by multiplying it by 60. After rounding to the nearest minute, we choose the correct option from the provided choices a) 4 hours 32 minutes, b) 5 hours 28 minutes, c) 5 hours 46 minutes, d) 6 hours 18 minutes.