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alexandr1967 [171]
3 years ago
11

Wanni cycled 6 km from her house to the school at a uniform speed, v km/h. If she increased her speed

Mathematics
1 answer:
Karolina [17]3 years ago
3 0

Answer:

The quadratic equation in terms of v is   v² + 2 v + 180 = 0

Step-by-step explanation:

Given as :

The distance between house to the school = d = 6 km

The uniform speed = v km/h

So, Time = \dfrac{\textrm Distance}{\textrm speed}

or, t = \dfrac{\textrm d}{\textrm v}

Or, t = \dfrac{\textrm 6}{\textrm v}

<u>Now, Again</u>

The speed is increase by 2 km/h

i.e speed = (v + 2) km/h

So, Time taken = t' = (t - \dfrac{4}{60})hours

i.e t' =  (t - \dfrac{1}{15})hours

Now, Time = \dfrac{\textrm Distance}{\textrm speed}

So, (t - \dfrac{1}{15}) = \dfrac{\textrm d}{\textrm v}

Or,  (t - \dfrac{1}{15}) = \dfrac{\textrm 6}{\textrm (v + 2)}

Or , \dfrac{\textrm 6}{\textrm v} -  \dfrac{1}{15} = \dfrac{\textrm 6}{\textrm (v + 2)}

Or , \dfrac{\textrm 90 - v}{\textrm 15 v} = \dfrac{\textrm 6}{\textrm v + 2}

Or, (90 - v) × (v + 2) = 6 × 15 v

Or, 90 v - 180 - v² - 2 v = 90 v

Or,  v² + 2 v + 180 = 90 v - 90 v

Or,  v² + 2 v + 180 = 0

So, The quadratic equation in terms of v

v² + 2 v + 180 = 0

Hence The quadratic equation in terms of v is   v² + 2 v + 180 = 0   Answer

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