The distance an automobile can travel in h hours at an average rate of 50 miles an hour is found y the formula d=50h. Problem: A car was driven for 3 hours. The driver then stopped 3/4 of an hour for lunch. After lunch he drove for 2 and 1/2 hours, then stopped 1/2 hr for a flat tire. After that he resumed driving the car. There is another car that starts from the same place 3 hrs after the first car and overtakes the first in 5hrs. Determine the rate of the second car. How far apart will the cars be 1 and 1/2 hours after the second car starts?
To find the rate of the second car, we'll first need to determine how far the first car traveled in 8 hours.
First, let's calculate the total time the first car spent driving:
3 hours + 3/4 hour for lunch + 2 1/2 hours + 1/2 hour for a flat tire = 6 3/4 hours
Now, we can substitute this total time into the formula d = 50h to find the distance traveled by the first car:
d = 50 * (6 3/4)
= 50 * (27/4)
= 675/2
= 337.5 miles
Therefore, the first car has traveled 337.5 miles in 8 hours.
Now, let's find the rate of the second car. We know that it overtakes the first car in 5 hours and starts from the same place. This means that the second car must have traveled the same distance as the first car in those 5 hours.
Since we know the distance, we can use the formula d = rt, where d is the distance, r is the rate, and t is the time.
For the second car, we can write the equation as:
337.5 = r * 5
Now, we can solve for r:
r = 337.5/5
= 67.5 mph
Therefore, the rate of the second car is 67.5 mph.
To find how far apart the cars will be 1 and 1/2 hours after the second car starts, we can calculate the distance the second car would have traveled in that time.
Using the formula d = rt for the second car:
d = 67.5 * 1 1/2
= 67.5 * (3/2)
= 101.25 miles
Therefore, 1 and 1/2 hours after the second car starts, it will be approximately 101.25 miles apart from the first car.