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By driving 8 mph faster than Bob, John can make a 230 mile trip in one half hour less. How fast does Bob drive on the trip? Round your answer to the nearest mile per hour. Enter only the numerical value in the answer box

Respuesta :

Answer: The speed of Bob is 56.8 km/hr.

Step-by-step explanation:

Let the speed of Bob be 'x'.

Let the speed of John be 'x-8'.

Distance covered = 230 miles

time = [tex]1\dfrac{1}{2}=\dfrac{3}{2}\ hr[/tex]

According to question, we get that

[tex]\dfrac{230}{x}-\dfrac{230}{x+8}=\dfrac{3}{2}\\\\230\dfrac{x+8-x}{x(x+8)}=\dfrac{3}{2}\\\\\dfrac{230\times 8}{x^2+8x}=\dfrac{3}{2}\\\\\dfrac{1840}{x^2+8x}=\dfrac{3}{2}\\\\1840\times 2=3x^2+24x\\\\3680=3x^2+24x\\\\3x^2+24x-3680=0\\\\x\approx 56.8\ km/hr[/tex]

Hence, the speed of Bob is 56.8 km/hr.

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