SOLUTION: A cyclist rides 30 miles at an average speed of 9 miles/hr. At what rate must the cyclist cover the next 10 miles in order to bring the overall average speed up to 10 miles/hr?

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Question 224698: A cyclist rides 30 miles at an average speed of 9 miles/hr. At what rate must the cyclist cover the next 10 miles in order to bring the overall average speed up to 10 miles/hr?
Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A cyclist rides 30 miles at an average speed of 9 miles/hr.
At what rate must the cyclist cover the next 10 miles in order to bring the
overall average speed up to 10 miles/hr?
:
Let s = speed required to accomplish this
:
In order accomplish this the total time for the 40 mi trip:
= 4 hrs
;
Write a time equation (time = ):
Time at 9 mph + time at s mph = 4 hrs
+ = 4
Multiply by 9s, results
30s + 9(10) = 9s(4)
30s + 90 = 36s
90 = 36s - 30s
90 = 6s
s =
s = 15 mph in order to average 10 mph
;
:
Check solution by finding the times = 4 hr
30/9 + 10/15 =
3.33 = .67 = 4 hrs

Answer by Edwin McCravy(20056) (Show Source):
You can put this solution on YOUR website!
A cyclist rides 30 miles at an average speed of 9 miles/hr. At what rate must the cyclist cover the next 10 miles in order to bring the overall average speed up to 10 miles/hr?

Make this chart: DISTANCE RATE TIME First part of trip 30 9 30/9 Last part of trip 10 R 10/R ------------------------------------------------- Whole trip 40 10 40/10 Let R be the rate required for the last part of the trip. So fill in the Distances and the rate Add the distances and get 40 miles. Fill that in: DISTANCE RATE TIME First part of trip 30 9 Last part of trip 10 R ------------------------------------------------- Whole trip 40 10 Use to fill in the times DISTANCE RATE TIME First part of trip 30 9 30/9 Last part of trip 10 R 10/R ------------------------------------------------- Whole trip 40 10 40/10 To get the equation, realize that TIME FOR FIRST PART + TIME FOR LAST PART = TOTAL TIME FOR TRIP Solve that and get R=15 miles/hr Edwin