Question

A man covered half of his journey at X km/he and the remaining at 4X km/hr. if his average speed for the entire journey was 38.4 km/he,what is the value of X.​

Answer 1

Given:

A man covered half of his journey at X km/hr and the remaining at 4X km/hr.

His average speed for the entire journey was 38.4 km/hr

To find:

What is the value of X?

Solution:

Let "D" represents the total distance travelled by the person.  

So,

The time taken by the man for the first half of his journey i.e., “D/2” with the speed of X km/hr = [$\frac{\frac{D}{2} }{X}$] hr

The time taken by the person for the other half of his distance “D/2” with a speed of 4X km/hr = [$\frac{\frac{D}{2} }{4X}$] hr

The average speed of the man = 36.8 km/hr

We know,

$\boxed{\bold{Average Speed = \frac{Total \:Distance }{Total \:Time \:taken} }}$

According to the above formula and the given values, we can write the equation as,

$\frac{\frac{D}{2} + \frac{D}{2} }{\frac{\frac{D}{2} }{X} + \frac{\frac{D}{2} }{4X} } = 38.4$

$\implies \frac{D}{\frac{\frac{D}{2} }{X} + \frac{\frac{D}{2} }{4X} } = 38.4$

$\implies \frac{D}{\frac{D}{2X} + \frac{D}{8X} } = 38.4$

$\implies \frac{1}{\frac{1}{2X} + \frac{1}{8X} } = 38.4$

$\implies \frac{8X^2}{4X + X } = 38.4$

$\implies \frac{8X^2}{5X} = 38.4$

$\implies 8X = 38.4 \times 5$

$\implies X = \frac{38.4 \times 5}{8}$

$\implies \bold{X = 24\:kh/hr}$

Thus, the value of X is → 24 km/hr.

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