Final answer:
Passenger A drove for 5 hours at an average speed of 70 mph during a 520-mile trip from Chicago to Springfield that took 8 hours in total, while Passenger B drove for the remaining time at an average speed of 55 mph.
Step-by-step explanation:
To determine how long Passenger A drove during the 520-mile trip from Chicago to Springfield at an average speed of 70 mph, while Passenger B drove at an average speed of 55 mph for the remaining time, we need to set up an equation using the given information. The total trip took 8 hours. We designate Passenger A's driving time as x hours and Passenger B's driving time as y hours.
Given:
- Passenger A's speed = 70 mph
- Passenger B's speed = 55 mph
- Total time for the trip = 8 hours
- Total distance = 520 miles
Since time is distance divided by speed, we can write the following equation for the total time of the trip:
x + y = 8 (1)
And since the distance is the speed multiplied by time, we can write another equation for the distances driven by both passengers:
70x + 55y = 520 (2)
To solve these equations simultaneously, we can express y in terms of x using equation (1):
y = 8 - x
Substituting y in equation (2), we get:
70x + 55(8 - x) = 520
70x + 440 - 55x = 520
15x + 440 = 520
15x = 520 - 440
15x = 80
x = 80 / 15
x = 5.33
However, since our options are whole numbers, we round x to the nearest whole number which is 5 hours.
Therefore, the correct answer is c) 5 hours.