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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.​

User Hailin Tan
by
7.8k points

1 Answer

5 votes

Answer:

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

User Martin Josefsson
by
7.9k points