3 years ago

I know what the answer is but the teacher wants me to explain helpppppp

Mathematics

1 answer:

adoni [48]3 years ago

3 0

answer: 8

Steps / explaination

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3 years ago

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

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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

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

$\dfrac{12}{x+1}+\dfrac{12}{x}=5.4.$

Solve this equation:

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

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

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4 years ago