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Ed is planning daily walking workouts on the same distance of 12 km in the morning and in the evening. Usually he is walking at constant rate, however he planned his rate to be 1 km/h more in the morning than in the evening. Given he is willing to spend 5 hours and 24 minutes daily on these workouts, what should his morning rate be, in km/h?

Respuesta :

frika

Answer:

5 km/h

Step-by-step explanation:

Let x km/h be Ed's rate in the evening, then x+1 km/h is his rate in the morning. It takes him

  • [tex]\dfrac{12}{x+1}[/tex] hours in the morning to pass 12 km;
  • [tex]\dfrac{12}{x}[/tex] hours in the evening to pass 12 km.

In total, it takes him 5 hours 24 minutes ([tex]5\dfrac{24}{60}=5.4[/tex] hours), then

[tex]\dfrac{12}{x+1}+\dfrac{12}{x}=5.4.[/tex]

Solve this equation:

[tex]\dfrac{12x+12(x+1)}{(x+1)x}=5.4,\\ \\12x+12x+12=5.4x^2+5.4x,\\ \\5.4x^2 -18.6x-12=0,\\ \\54x^2-186x-120=0,\\ \\9x^2 -31x-20=0,\\ \\D=(-31)^2-4\cdot 9\cdot (-20)=1,681=41^2,\\ \\x_{1,2}=\dfrac{-(-31)\pm\sqrt{41^2}}{2\cdot 9}=\dfrac{31\pm41}{18}=-\dfrac{5}{9},\ 4\ km/h.[/tex]

Ed's rate cannot be negative, thus x=4 km/h. His morning rate is x+1=5 km/h.

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