Final answer:
To find the number of hours after leaving the rest stop that the car had an average speed of 34 miles per hour, set up an equation using the average speed formula, solve for x, and find that x equals 16.5 hours. However, this result should be double-checked for accuracy due to its unusually high value.
Step-by-step explanation:
To answer the question: How many hours after leaving the rest stop did the car have an average speed of 34 miles per hour? We can use the formula for average speed which is total distance divided by total time. The car traveled 17.5 miles in the first hour due to heavy traffic. For the car to have an average speed of 34 miles per hour, we need to calculate the total distance it would have covered at that average speed for the total time taken.
Let x be the number of hours the car traveled at 35 miles per hour after the first hour. Hence, the total distance the car would have covered after x hours is 17.5 + 35x miles. The total time taken will then be 1 + x hours. Using the formula for average speed:
Average Speed = Total Distance / Total Time
34 miles/hr = (17.5 + 35x) / (1 + x)
We solve this equation to find the value of x, which would be the number of hours the car traveled at 35 miles per hour after the first hour to achieve an average speed of 34 miles per hour.
If we cross-multiply and solve for x, we get:
34(1 + x) = 17.5 + 35x
34 + 34x = 17.5 + 35x
34x - 35x = 17.5 - 34
-x = -16.5
x = 16.5 hours
Therefore, the car would have to travel for 16.5 hours at 35 miles per hour after the first hour to have an average speed of 34 miles per hour. However, as this is a high number that may seem unrealistic for actual driving conditions,