Question

A boat starts with the speed of 1km per hour. After every 1km, the speed of boat becomes twice. How much will be average speed of the boat at the end of the journey of 2.5 km ?

(A)
$\frac{2.5}{1.5125}$
km/hr
(B)
$\frac{2.5}{1.75}$
km/hr
(C)
$\frac{2.5}{1.625}$
km/hr
(D)
$\frac{2.5}{1.50}$
km/hr

Please give answer with full explanation and the fastest and most correct answer = Brainliest Answer ☺

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Answer 1

Answer:

Option => C.

$\sf \dfrac{2.5}{1.625}\;km/hr$

Explanation :

Given :

A boat starts with the speed of 1km per hour.

After every 1km, the speed of boat becomes twice.

To Find :

The Average Speed.

Solution :

We know that :

$\bigstar\;\boxed{\sf Speed = \dfrac{Distance}{Time}}}$

$\bigstar\;\boxed{\sf Time = \dfrac{Distance}{Speed}}}$

So,

$\sf\\ \\ \implies t_1 = \dfrac{1\;km}{1\;km/hr}\qquad [Here\;'km'\;cancellled\;each\;other.]\\ \\ \\ \implies t_1 = 1\;hr$

Now,

$\sf\\ \\\implies t_2 = \dfrac{1}{2}\;hr.$

$\sf\\ \\\implies t_3 = \dfrac{0.5\;km}{4\;km/hr}\qquad [Here,\;'km'\;cancelled\;each-other]\\ \\ \\\implies t_3 = \dfrac{1}{8}\;hr.$

Now,

$\textbf{Total Time = } \dfrac{1+1}{8}\;+\;\dfrac{1}{8}\\ \\ \\\implies \dfrac{8+4+1}{8}=\dfrac{13}{8}=1.625\\ \\ \\\implies t = 1.625$

We know that :

$\bigstar\;\boxed{\sf Average\;Speed = \dfrac{Total\;Distance}{Total\;Time}}$

So,

$\sf\\ \\\implies \dfrac{2.5}{1.625}$

∴ The answer is $\sf \dfrac{2.5}{1.625}$