Question

a man travels 600 km (apart) by train and partly by car.it takes 8 hours and 40 min if he travels 320km by train and the rest by car.it would take 30 min more if he travels 200 km by train and the rest by car. find the speed of train and the car separately

Answer 1

Hope it helps you.

Please mark as the brainliest

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

Man travelled 600 km partly by train and car.

It takes 8 hr 40 min if he travels 320 km by train and rest by car.

It would take 30 min more if he travels 200 km by train and rest by car.

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

Speed of car

Speed of train

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let 'x' be the speed of train and 'y' be the speed of car.

$\:\:$

Total distance travelled is 600 km.

$\:\:$

The time taken by the man to travel 320 km by train in is:

$\:\:$

⇛ $\rm \dfrac { 320 } { x }$

$\:\:$

The time taken by the man to travel 280 km by car is:

$\:\:$

⇛ $\rm \dfrac { 280 } { y }$

$\:\:$

Hence the total time taken by the man to travel 600 km is :

$\:\:$

⇛ $\rm \dfrac { 320 } { x }$ + $\rm \dfrac { 280 } { y }$

$\:\:$

Given that the total time is 8 hours 40 minutes :

$\:\:$

⇛ $\sf \dfrac { 26 } { 3 } hrs$

$\:\:$

$\underline{\bold{\texttt{Thus, we have,}}}$

$\:\:$

⇛ $\rm \dfrac { 320 } { x }$ + $\rm \dfrac { 280 } { y }$ = $\sf \dfrac { 26 } { 3 } hrs$ ---------(1)

$\:\:$

The time taken by the man to travel 200 krm by train is:

$\:\:$

⇛ $\rm \dfrac { 200 } { x }$

$\:\:$

The time taken by the man to travel 400 km by car is:

$\:\:$

$\rm \dfrac { 400 } { y }$

$\:\:$

Hence the total time taken by the man to travel 600 km is:

$\:\:$

⇛ $\rm \dfrac { 200 } { x }$ + $\rm \dfrac { 400 } { y }$

$\:\:$

Given that the total time is 30 minutes more than 8 hours 40 minutes:

$\:\:$

⇛ $\rm 8 \frac { 2 } { 3 } + \frac { 30 } { 60 } = \frac { 55 } { 6 }$

$\:\:$

$\underline{\bold{\texttt{Thus, we have,}}}$

$\:\:$

⇛ $\rm \dfrac { 200 } { x }$ + $\rm \dfrac { 400 } { y }$ = $\rm \frac { 55 } { 6 }$ --------(2)

$\:\:$

Substitute $\rm \dfrac {1 } { x }$ = u & $\rm \dfrac { 1 } { y }$ = v

$\:\:$

Thus equation (1) & (2) can be rewritten as :

$\:\:$

⇛ $\sf 320u + 280v = \dfrac { 26 } { 3 }$

$\:\:$

⇛ $\sf 200u + 400v = \dfrac { 55 } { 6 }$

$\:\:$

Solving the above equations we have,

$\:\:$

⇛ $\tt u = \frac { 1 } { 80 }\: \&\: v = \frac { 1 } { 60 }$

$\:\:$

Thus the speed of the train and car are respectively , 80 km/hr & 60 km/hr.