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Nikolay [14]
3 years ago
10

I promise I will mark as brainiest if a speed of a car increase its average speed in a journey of 200 miles by 5 mile/hour the j

ourney will end with a difference of one hour less, so what is the original speed of the car ?
Mathematics
1 answer:
jok3333 [9.3K]3 years ago
7 0

Answer:

\large \boxed{\sf \ \ \ \dfrac{\sqrt{4025}-5}{2}=29.22144... \ \ \ }

Step-by-step explanation:

Hello

<u>Let's note the original speed of the car v</u>

it means that in 1 hour he is going v miles

so to go 200 miles it takes ( in hour)

\dfrac{200}{v}

If the speed of the car is v+5 than to go 200 miles it takes (in hour)

\dfrac{200}{v+5}

and this time is one hour less so we can write

\boxed{\sf \ \ \dfrac{200}{v+5}=\dfrac{200}{v}-1 \ \ }

We can multiply by v(v+5) both parts of the equation so

200v=200(v+5)-v(v+5)\\\\200v=200v+1000-v^2-5v\\\\v^2+5v-1000=0

\Delta=b^2-4ac=5^2+4*1000=4025\\\\ \text{There are potential solutions }\\\\\ \ \ \ \ x_1=\dfrac{-5-\sqrt{4025}}{2}\\\\\ \ \ \ \ x_2=\dfrac{-5+\sqrt{4025}}{2}

Only one is positive and this is is

x_1=\dfrac{\sqrt{4025}-5}{2}=29.22144...

So the original speed is 29.22144... mph

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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