<PRE><B>Question 617105</B>
you are running a 6000 meter race. 
your average speed in the first half of the race is 50 meters per minute faster than your average speed in the second half.
 you finish the race in 27 minutes. what is your average speed in the second half of the race?
:
Write a time equation, time = dist/speed
:
Let s = av speed in the 2nd half
then
(s+50) = av speed in the 1st half
:
2nd half time + 1st half time = 27 min
{{{3000/s}}} + {{{3000/((s+50))}}} = 27
:
multiply by s(s+50) to clear the denominators, results:
3000(s+50) + 3000s = 27s(s+50)
3000s + 150000 + 3000s = 27s^2 + 1350s
:
Combine like terms on the right
0 = 27s^2 + 1350s - 6000s - 150000
;
A quadratic equation
27s^2 - 4650s - 150000 = 0
You can solve this using the quadratic formula; a=27, b=-4650, c=-150000
:
you should get a positive solution:
 s = 200 m/sec, speed the 2nd half
:
:
Check this solution in the equation
{{{3000/200}}} + {{{3000/((250))}}} = </PRE>