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?
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time = distance/rate
Total time = 15/x + 11/(x-2)
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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)
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c. i) simplify your equation and show that it can be written as 
2x^2-17x+15=0 
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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
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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)
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Cheers,
Stan H.