Carmina travels 120 miles, the first 40 miles at miles per hour and the remaining 80 miles at miles per hour. What is her average speed, in miles per hour, for the entire trip in terms of and ?
Question
Carmina travels 120 miles, the first 40 miles at miles per hour and the remaining 80 miles at miles per hour. What is her average speed, in miles per hour, for the entire trip in terms of and ?
Solution
To calculate the average speed, we need to know the total distance traveled and the total time taken.
The total distance traveled by Carmina is 120 miles.
The time taken for the first 40 miles = 40 / v (where v is the speed for the first 40 miles) The time taken for the next 80 miles = 80 / u (where u is the speed for the next 80 miles)
The total time taken = (40/v) + (80/u)
The average speed is then calculated by dividing the total distance by the total time.
So, the average speed = Total distance / Total time = 120 / [(40/v) + (80/u)]
This is the average speed of Carmina's trip in terms of v and u.
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