Segment ab falls on line 6x + 3y = 12. segment cd falls on line 4x + 2y = 8. what is true about segments ab and cd?

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Ответ:

janrusk3983

31.10.2022

Mathematics

1.67 hours

Step-by-step explanation:

Let the original speed of Jonathan = units/hr

Let the original time taken by Jonathan = hours

Let the distance = units

Formula for distance is given as:

$Distance = Speed \times Time$

Given that half the distance is covered by original speed.

$\Rightarrow \dfrac{D}{2} = \dfrac{x}{2}\times \dfrac{y}{2}\\\Rightarrow D = \dfrac{xy}{2} ..... (1)$

Half the distance is covered by increasing the rate by 25%.

i.e. increased speed:

$\dfrac{5}{4}x\ units/hr$

Hence, Time taken:

$\dfrac{y}{2}-\dfrac{1}{2}$

Distance traveled is half of the total distance:

$\Rightarrow \dfrac{D}{2} = \dfrac{5x}{4}\times (\dfrac{y}{2}-\dfrac{1}{2})\\\Rightarrow D = \dfrac{5x}{2}\times (\dfrac{y}{2}-\dfrac{1}{2}) .... (2)$

Dividing (1) by (2):

$\dfrac{xy\times 4}{2\times 5x(y-1)} = 1\\\Rightarrow 2y=5y-5\\\Rightarrow 3y=5\\\Rightarrow y =1.67\ hours$

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