amy wants to travel from elmtown to lakeside at an average speed of 50 miles/hour. she travels half the distance and discovers that her average speed has been only 25 miles/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?
she has gone half the distance at half of her desired speed
she has used up all the time needed for her desired trip
she needs to be at lakeside NOW ... magic maybe?
(25 + (50+x))/2 = 50.
(75 + x)/2 = 50,
75+x = 100,
X = 25 mi/h.
50 + x = 50 + 25 = 75 mi/h during 2nd half of trip.
To solve this problem, let's break it down step by step:
1. Let's assume the total distance from Elmtown to Lakeside is "D" miles.
2. Amy travels half the distance, which is D/2 miles, at an average speed of 25 miles/hour. This means the time taken for this part of the trip is (D/2) / 25 hours.
3. Now, let's calculate the time taken for the remaining part of the trip. Amy needs to travel the remaining distance, which is also D/2 miles, at a speed that will allow her to average 50 miles/hour for the entire trip.
4. We know the formula for average speed is total distance divided by total time. We can rearrange this formula to solve for time: time = distance / speed.
5. We can calculate the time taken for the remaining part of the trip using the average speed formula: (D/2) / 50.
6. Now, we know that the total time taken for the entire trip is the sum of the time for the first half and the time for the remaining part: (D/2) / 25 + (D/2) / 50.
7. We want the average speed for the entire trip to be 50 miles/hour, so we can set up the equation: D / ((D/2) / 25 + (D/2) / 50) = 50.
8. Simplifying the equation, we get: D / ((2D + D)/100) = 50.
9. Further simplification gives us: D / (3D/100) = 50.
10. Cross-multiplying, we get: 100D = 50 * 3D.
11. Dividing both sides by D, we get: 100 = 150/3.
12. Solving the equation, we find: D = 1.5 miles.
So, Amy needs to travel the remaining 1.5 miles at a speed that will allow her to average 50 miles/hour for the entire trip.