SOLUTION: Zarig took part in a 26 mile road race. a. he ran the first 15 miles at an average speed of x mph. he ran the last 11 miles at an average speed of (x-2)mph. write down an expres

Question 167548: Zarig took part in a 26 mile road race.
a. he ran the first 15 miles at an average speed of x mph. he ran the last 11 miles at an average speed of (x-2)mph. write down an expression,in terms of x, for the time he took to complete the 26 mile race?
b.zarig took 4 hours to complete the race. using your answer to part a, form an quation in terms of x.
c. i) simplify your equation and show that it can be written as
2x^2-17x+15=0
ii) solve the quation and obtain zarig's average speed over the first 15 miles of the race.

pls it would kind enough if you can help me put with this question?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Zarig took part in a 26 mile road race.
a. he ran the first 15 miles at an average speed of x mph. he ran the last 11 miles at an average speed of (x-2)mph. write down an expression,in terms of x, for the time he took to complete the 26 mile race?
-------
time = distance/rate
Total time = 15/x + 11/(x-2)
-----------------------------------
b.zarig took 4 hours to complete the race. using your answer to part a, form an equation in terms of x.
4 = 15/x + 11/(x-2)
------------------------
c. i) simplify your equation and show that it can be written as
2x^2-17x+15=0
---------
4 = 15/x + 11/(x-2)
4x(x-2) = 15(x-2) + 11x
4x^2-8x = 15x-30 + 11x
4x^2-34x-30 = 0
2x^2-17x-15 = 0
---------------------------
ii) solve the equation and obtain zarig's average speed over the first 15 miles of the race.
x = [17 +- sqrt(17^2-4*2*-15)]/4
x = [17 +- sqrt(409)]/4
x = [17 +- 20.2237..]/4
Positive solution:
x = 9.306 mph (average speed over the 1st 15 miles)
===================
Cheers,
Stan H.

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