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

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

Explanation:

Given as :

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

The uniform speed = v km/h

So, Time =
`(\textrm Distance)/(\textrm speed)`

or, t =
`(\textrm d)/(\textrm v)`

Or, t =
`(\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 -
`(4)/(60)`)hours

i.e t' = (t -
`(1)/(15)`)hours

Now, Time =
`(\textrm Distance)/(\textrm speed)`

So, (t -
`(1)/(15)`) =
`(\textrm d)/(\textrm v)`

Or, (t -
`(1)/(15)`) =
`(\textrm 6)/(\textrm (v + 2))`

Or ,
`(\textrm 6)/(\textrm v)` -
`(1)/(15)` =
`(\textrm 6)/(\textrm (v + 2))`

Or ,
`(\textrm 90 - v)/(\textrm 15 v)` =
`(\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