Question

Man cover half of his journey by train at 60kmph, half the remaining journey by bus at 30kmph & rest by cycle at 10kmph find the average speed during entire journey

Answer 1

Answer:

24 mi/h

Step-by-step explanation:

Answer 2

Given:

Man covers:

half journey by train at 60 km/hr

half the remaining journey by bus at 30 km/hr

rest by cycle at 10 km/hr

To find:

The average speed during entire journey

Concept to be used:

$\boxed{Time \:= \frac{Distance}{Speed}}$

and

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

Solution:

Let "D" be the total distance covered by the man during the entire journey

Therefore,

The distance traveled by train = $\frac{D}{2}$km

The distance traveled by bus = $\frac{1}{2} [D - \frac{D}{2}]$ = $\frac{D}{4}$ km

The distance traveled by cycle = $D - \frac{D}{2} - \frac{D}{4}$ = $\frac{D}{4}$ km

So, we have

The time taken by man while travelling by train = $\frac{\frac{D}{2}}{60}$ = $\frac{D}{120}$ hrs

The time taken by man while travelling by bus = $\frac{\frac{D}{4}}{30}$ = $\frac{D}{120}$ hrs

The time taken by man while travelling by cycle = $\frac{\frac{D}{4}}{10}$ = $\frac{D}{40}$ hrs

∴ Total time taken by the man to cover the entire journey is,

= $\frac{D}{120} + \frac{D}{120} + \frac{D}{40}$

= $\frac{D \:+\: D\: +\: 3D}{120}$

= $\frac{5D}{120}$

= $\frac{D}{24} \:hr$

Now, using the formula of the average speed above, we get

The average speed is,

= $\frac{Total\:distance\:covered \:during\:the \:entire\:journey}{Total \:time\:taken\:to \:cover\: the\: entire\: journey}$

= $\frac{D}{\frac{D}{24}}$

= $\frac{1}{\frac{1}{24}}$

= $\bold{24\:km/hr}$

Thus, the average speed during entire journey is 24 km/hr.

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