Question

Question 1 A REVISIT a a Usually a cyclist takes a certain amount of time to travel from a park to his house. One particular day, the wind blew towards his direction of journey. If the wind's rate was 2/3rd of that of the cyclist and it helps save 16 minutes of his journey time, then what is his usual time to cover the journey? Answer choices Select only one option O 14 minutes O 24 minutes 0 60 minutes O. 40 minutes​

Answer 1

Answer:

Explanation:

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Answer 2

Given,

The speed of the wind is = $\frac{2}{3}$(speed of cyclist)

The time saved in the journey due to wind's favor = 16 minutes

To Find,

The usual time the cyclist takes to cover the journey in the absence of wind's favor.

Solution,

Let the distance traveled be $d$.

Let the speed of the cyclist be $x$.

Then the speed of wind = $\frac{2}{3} (speed of cyclist)$

⇒$\frac{2}{3}(x) = \frac{2}{3} x$

Thus, the speed of wind is $\frac{2}{3} x$.

Let the time taken for the cyclist alone to cover the distance be $t$.

The distance traveled can be calculated by using the formula,

$Distance = (speed)(time)$

∴The distance traveled by the cyclist without the wind's favor, $d$ = $xt$

Then the distance traveled by the cyclist with the wind's favor can be written as, $d = (\frac{2x}{3}+x )(t-16)$

⇒ $d = (\frac{2x+3x}{3} )({t-16})$

⇒$d = \frac{5x}{3}(t-16)$

The distance traveled is the same in both cases.

∴${x}{t} = \frac{5x}{3}(t-16)$

Since $x$ can be canceled on both sides, the equation can be rewritten,

⇒ $t = \frac{5}{3}(t-16)$

⇒$3t = 5(t-16)$

⇒$3t = 5t-80$

⇒$5t-3t = 80$

⇒$2t =80$

⇒$t =\frac{80}{2} = 40$

Henceforth, the time taken by the cyclist to cover the journey without wind's favor is 40 minutes.