Question

Please solve Q no. 40 fast! will mark you the brainliest.

Answer 1

Heya here is ur answer-

Let the speed of the train be x km/hr and that of the car be y km/hr.

ACCORDING TO CONDITION 1st-

Distance travelled by train=250 km.

Distance travelled by car=(370-250)=120 km.

Total time taken to cover the journey=4 hours.

We know that -

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

therefore,

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

Time taken to travel 250 km by train-

$= \frac{250}{x} hour$

Time taken to travel 120 km by car-

$= \frac{120}{y} \: hour$

therefore,

$\frac{250}{x} + \frac{120}{y} = 4.......(i)$

ACCORDING TO CONDITION 2nd-

Distance travelled by train=130 km.

Distance travelled by car=(370-130)=240 km.

Total time taken to cover the journey=4 hours + 18 mins

$= 4 + \frac{18}{60} \\ = \frac{240 + 18}{60} \\ = \frac{258}{60} = \frac{43}{10} \: hour$

therefore,

$\frac{130}{x} + \frac{240}{y} = \frac{43}{10} ......(ii)$

Let 1/x = p and 1/y = q.

Then , equation (i) will be-

$250p + 120q = 4.......(iii)$

and equation (ii) will be -

$130p + 240q = \frac{43}{10}....... (iv)$

Multiplying eq. (iii) by 2 and then subtracting from eq. (iv)-

$1300p + 2400q = 43 - (5000p + 2400q )= 80$

we will get-

$- 3700p = - 37 \\ p = \frac{ - 37}{ - 3700} \\ p = \frac{1}{100}$

but p = 1/x.

therefore,

$\frac{1}{x} = \frac{1}{100} \\ x = 100 \: km \: per \: hour$

Now put p = 1/100 in equation (

iii)-

$\frac{250}{100} + 120q = 4 \\ 120q = 4 - \frac{250}{100} \\ 120q = 4 - 2.5 \\ q = \frac{1.5}{120} \\ q = \frac{15}{1200} \\ q = \frac{1}{80}$

but we know that q= 1/y.

therefore,

$\frac{1}{y} = \frac{1}{80} \\ y = 80 \: km \: per \: hour$

Hence, the speed of the train is 100 km/hour and the speed of the car is 80 km/hour.

Answer 2

Answer:

100km/hr, 80km/hr

Step-by-step explanation:

Let the speed of the train = x km/hr.

Let the speed of the car = y km/hr.

(i) 250 km by train and rest by car. it takes 4 hours.

250 - > Train

370 - 250 = 120 - > Car

∴ Time = Distance/Speed

⇒ (250/x) + (120/y) = 4

(ii) Travels 130 km by train and rest by car, takes 18 minutes.

⇒ (130/x) + (240/y) = 4 + 18/60

⇒ (130/x) + (240/y) = 43/10

Now,

On solving (i) * 4 & (ii), we get

⇒ (130/x) + (240/y) = 43/10

⇒ (500/x) + (240/y) = 8

   ------------------------------------

   (370/x) = 37/10

       x = 100 km/hr

Substitute x = 100 km/hr in (ii), we get

⇒ (130/x) + (240/y) = 43/10

⇒ (130/100) + (240/y) = 43/10

⇒ (240/y) = (43/10) - (130/100)

⇒ 3y = 240

⇒ y = 80

Therefore:

Speed of the train = 100 km/hr.

Speed of the car = 80 km/hr.

Hope it helps!