Final answer:
The distance from Shelbyville to Springfield is calculated using the difference in arrival times and speeds of the two cars, resulting in approximately 29.3 miles.
Step-by-step explanation:
To calculate the distance from Shelbyville to Springfield, we need to make use of the speed and time difference for the two cars to arrive at their destination. Given that the first car travels at a constant speed of 50 mph and arrives at 1:00 PM, and the second car travels at a speed of 30 mph and arrives at 1:22 PM, we can determine that the time difference between their arrivals is 22 minutes.
First, let's convert 22 minutes to hours, since we are dealing with speeds in miles per hour (mph).
22 minutes = 22/60 hours = 11/30 hours.
Now, since the second car travels at 30 mph and takes 11/30 hours longer, we can calculate the distance (D) it traveled during that time:
D = speed × time
D = 30 mph × 11/30 hours
D = 11 miles.
This means that the first car had already covered 11 miles by the time the second car arrives. Given that the first car travels at 50 mph, we can calculate the total distance (T) from Shelbyville to Springfield as follows:
T = 11 miles + (distance the first car travels in 11/30 hours)
T = 11 miles + (50 mph × 11/30 hours)
T = 11 miles + 18.3 miles
T = 29.3 miles.
Therefore, the distance from Shelbyville to Springfield is approximately 29.3 miles.