Question

A motor cyclist completes a certain journey in 5 hours. he covers one-third distance at 60 km/hr and the rest at 80 km/hr. the length of journey is

Answer 1

Motion,

We have,

Here the total time = 5 hours
Let the length of the journey = x km.

And let the time taken to go ⅓ of the distance = y hr.
So y × 60 = x/3
or, y = x/180.......(1)

Also let the time taken for rest of the journey i.e.⅔ of the journey = z hr.
So, z × 80 = 2x/3
or, z = x/120......(2)

Now y + z = 5 [placing the values from equations 1 and 2 we get,
(x/180) + (x/120) = 5
or, (2x + 3x)/360 = 5
or, 5x = 5×360
or, x = 360 km
Therefore the length of the journey = 360 km.

That's it
Hope it helped (^_^メ)

Answer 2

AnswEr:

GivEn:

• Time = 5 hours
• ⅓ at 60 km/h
• Rest at 80 km/h

To Find:

• Total Distance - ?

Solution:

Let the total distance be x km.

Then,

Time taken to cover $\sf { \dfrac{x}{3} }$ is $\sf { \dfrac{x/3}{3} }$

:- Time to cover remaining distance - $\sf { \dfrac{2}{3} x}$km is $\sf { \dfrac{2x/3}{80} }$ hour.

$\sf\bf\underline\blue{ Step\:by\: step:-}$

According to the given Condition,

$\implies{\boxed{\sf{ \dfrac{x/3}{60} + \dfrac{2x/3}{80} = 5 }}}$

$\implies{\sf{ \dfrac{x}{180} + \dfrac{x}{120} = 5}}$

$\implies{\sf{ x( \dfrac{2+3}{360} ) = 5}} \\ \\ \implies{\sf{ 5x = 5 \times 360}} \\ \\ \implies{\sf{ x = \dfrac{ \cancel{5} \times 360}{ \cancel{5}} }} \\ \\ \implies\sf\underbrace{ \: \: x = 360\: \: km \: \: }$

Hence,

The length of journey is 360 km.

Extra Dose:

• Speed = Distance/Time

• Conversion of Km/h into m/sec = 5/18 m/sec

• Conversion of m/sec into km/h = 18/5 km/h