Question

a person travel half of the diatance at the speed of x km/h and remaining half of distance at 4x km / hour. find the value of x. if the average speed is 36.8 km /hour

Answer 1

If a person travels half of the journey at a speed of x km/hr and other with 4x km/hr and his average speed is 36.8 km/hr then the value of x is 23 km/hr.

Step-by-step explanation:

Let the total distance travelled by the person be “d” km.  

So, time taken by the person for the first half of his distance “d/2” with a speed of x km/hr = [$\frac{\frac{d}{2}}{x}$] hr

And, 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 person = 36.8 km/hr

Required formula:

Average speed = [Total distance] / [Total Time]

According to the formula and the given values, we can write the eq. as,

$\frac{d}{\frac{\frac{d}{2}}{x} + \frac{\frac{d}{2}}{4x}}$ = 36.8

⇒ $\frac{d}{\frac{d}{2x} + \frac{d}{4x}}$ = 36.8

⇒ $\frac{8x * 2x}{8x+2x}$ = 36.8

⇒ 16 x = 36.8 * 10

⇒ x = 368 / 16

⇒ x = 23 km/hr

Thus, the value of x is 23 km/hr.

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