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?
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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 {{{time=(distance)/(rate)}}} 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

{{{30/9+10/R=40/10}}}
{{{10/3+10/R=4}}}

Solve that and get R=15 miles/hr

Edwin</pre>