Question

A man travel 370km partly by train and partly by car if he covers 250km by train and the rest by car,he takes 4hours.But if he travel 130km by train and rest by car,he takes 18minutes more. Find the speed of the train and car.​

Answer 1

Answer:

Let the speed of the car be C kmph

Let the speed of the train be T kmph

4 hours = 250 km / T kmph + (370 - 250) km / C kmph

4 = 250/T + 120/C -- equation 1

4 hrs 18 minutes = 130 km / T kmph + (370 - 130)km / C kmph

258/60 = 4.3 = 130 / T + 240 / C --- equation 2

Multiply equation 1 by 2 and subtract equation 2 from it.

8 - 4.3 = 500/T - 130/T + 240/C - 240/C

3.7 = 370 / T

T = 370/3.7 = 100 kmph

Substitute the value of T in equation 1 to get,

4 = 250/T + 120/C -- equation 1

4 = 250/100 + 120/C

4 - 2.5 = 120/C

C = 120/1.5 = 80 kmph

The train runs at 100 kmph and the car runs at 80 kmph

Answer 2

$\huge\bigstar\mathfrak\blue{\underline{\underline{SOLUTION:}}}$

Let the speed of a train= x km/hr &

Let the speed of a train= x km/hr &the speed of a car= y km/hr

Total distance travelled= 370km

A/q

If he covers 250km by train & rest by car i.e.(370-250)= 120km

Time taken 4 hrs

If he travels 130km by train & rest by car i.e. (370-130)= 240km.

He takes 18m longer i.e.

$4 + \frac{18}{60} = 4.3hrs$

So, total time=train time+ car time

We know that,

$time = \frac{distance}{speed}$

$= > \frac{250}{x} + \frac{120}{y} = 4.........(1) \\ \\ = > \frac{130}{x} + \frac{240}{y} = 4.3......(2) \\ \\ let \: take \: \frac{1}{x} = u \: and \: \frac{1}{y} = v$

250u+120v= 4........(3)&

250u+120v= 4........(3)&130u+240v= 4.3......(4)

On multiplying equation (3) by 2

=) 500u+240v= 8.......(5)

On subtracting equation (4) from (5), we get

500u+240v-130u-240v= 8-4.3

=) 370u= 3.7

=) u= 3.7/370

=) u= 1/100

On putting the value of u in equation (4), we get

$= > 130( \frac{1}{100} ) + 240v = 4.3 \\ \\ = > 1.3 + 240v = 4.3 \\ \\ = > 240v = 3 \\ \\ = > v = \frac{3}{240} = \frac{1}{80} \\ \\ = > v = \frac{1}{80}$

So, we get u= 1/100 & v= 1/80

x= 100 & y= 80

Hence, the speed of the train is 100km/hr & the speed of the car is 80km/hr.

hope it helps ☺️