Question

Wanni cycled 6 km from her house to the school at a uniform speed, v km/h. If she increased her speed
by 2 km/h, she would arrive at the school 4 minutes earlier. Form a quadratic equation in term of v.​

Answer 1

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 = $\dfrac{\textrm 6}{\textrm v}$

Now, Again

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