Reposting see if someone else comes up with a different answer.
Amy wants to travel from Elm town to Lakeside at an average speed of 50 miles per hour. She travels half the distance and discovers that her average speed has only been 25 miles per hour. How fast must she drive for the remaining part of the trip if she is to average 50 miles per hour for the entire trip?
Trick question.
She travelled half the distance in 1 hour. ( time = distance/rate = 25 miles/(25 mph) = 1 hr)
To average 50 mph for the entire 50 miles would take 1 hour.
Amy has already used up all her time, can't be done
Here was Scott's answer.
"scott Monday, May 7, 2018 at 8:09pm
let's call the distance d
so the desired time for Amy's trip is ... d / 50
her time at the halfway point is ... (d / 2) / 25 , which equals ... d / 50
she has run out of time to achieve her desired average speed
I figured it just wasn't a possible answer. SORRY
Should have realized a bonus problem is sometimes a trick problem.
Sorry I wasted your time
To find how fast Amy must drive for the remaining part of the trip to average 50 miles per hour for the entire journey, we can use the concept of average speed.
Let's assume the total distance between Elm town and Lakeside is D miles. Amy travels half the distance, which is D/2 miles, at an average speed of 25 miles per hour. This means she takes (D/2) / 25 = D/50 hours to travel this distance.
Now, for the remaining half of the distance, Amy needs to travel D/2 miles in order to average a speed of 50 miles per hour for the entire trip. Let's call the remaining time T (in hours) it takes for her to cover this distance.
We can set up the equation: remaining distance / remaining time = 50 miles per hour.
D/2 / T = 50
Simplifying the equation, we get:
D/2 = 50T
Divide both sides of the equation by 50:
D/100 = T
Thus, Amy must drive the remaining half of the distance (D/2) in T = D/100 hours to average 50 miles per hour for the entire trip.