<PRE><B>Question 224698</B>
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:
{{{40/10}}} = 4 hrs
;
Write a time equation (time = {{{ dist/speed}}}):
Time at 9 mph + time at s mph = 4 hrs
{{{30/9}}} + {{{10/s}}} = 4
Multiply by 9s, results
30s + 9(10) = 9s(4)
30s + 90 = 36s
90 = 36s - 30s
90 = 6s
s = {{{90/6}}}
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
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