Maria drove to a ski resort that was 60 miles away. She decided to stop for lunch when she was 3/4 of the way there. If she drove for 9 hours before stopping for lunch, what was her average speed, in miles per hour?
3/4 of 60 is 45 mi
45mi/9hr = 5 mi/hr
what was she driving, a roller skate?
To find Maria's average speed, we need to divide the total distance she traveled by the total time it took her to travel that distance.
First, we need to determine the total distance Maria traveled. We know that the ski resort is 60 miles away and that she stopped for lunch when she was 3/4 of the way there.
If she stopped when she was 3/4 of the way, this means she traveled (1 - 3/4) = 1/4 of the total distance after lunch. Therefore, the distance she traveled before lunch is 3/4 * 60 miles = 45 miles.
So, Maria traveled a total of 45 miles before stopping for lunch, and 60 - 45 = 15 miles after lunch.
Now, we need to calculate the total time it took Maria to travel this distance. We are given that Maria drove for 9 hours before stopping for lunch.
To find her total travel time, we need to add the time she spent before lunch to the time she spent after lunch. Since we know the distance traveled and the average speed remains constant, the time can be found using the formula: time = distance / speed.
For the time before lunch, we have time = 45 miles / speed, and for the time after lunch, we have time = 15 miles / speed.
The total travel time is 9 hours, so we can write the equation: 9 = (45 / speed) + (15 / speed).
Now, we can solve this equation to find Maria's average speed.
Multiplying through by the common denominator (speed), the equation becomes: 9 * speed = 45 + 15.
Combining like terms, 9 * speed = 60.
Finally, we divide both sides by 9 to solve for Maria's average speed: speed = 60 / 9.
Calculating the result gives us Maria's average speed: speed = 6.67 miles per hour.
Therefore, Maria's average speed was approximately 6.67 miles per hour.