Question

if a train runs at 40 kmph it reaches its destination late by 11 minutes but if it runs at 50 km pH it is late by 5 minutes only find the distance to be covered by the train​

Answer 1

Answer:

$\bigstar{\bold{Distance\:to\:be\:covered=20\:km}}$

Step-by-step explanation:

$\Large{\underline{\bf{Given:}}}$

• If a train runs at a speed of 40 km/hr it reaches the destination late by 11 mins
• If a train runs at a speed of 50 km/hr, it reaches the destination late by 5 mins

$\Large{\underline{\bf{To\:Find:}}}$

• The distance to be covered by the train

$\Large{\underline{\bf{Solution:}}}$

➛ Let the time taken by the train to reach normally be x mins

➛ We know that,

   Distance = Speed × Time

➛ By first case,

   If train travels at the speed of 40 km/hr it takes 11 mins more than the normal time

   11 mins = 11/60 hours

➛ Hence,

   Distance = 40 × (x + 11/60)

   Distance = 40 × (60x +11)/60

   Distance = (120x + 22)/3--------(1)

➛ By second case given,

   If the train travels at a speed of 50 km/hr, it takes 5 mins more than the normal time.

   5 mins = 5/60 hours

➛ Therefore,

    Distance = 50 (x + 5/60)

    Distance = 50 × (60x + 5)/60

   Distance = (300x + 25)/6-----(2)

➛ Equating equations 1 and 2,

   (120x + 22)/3  = (300x + 25)/6

   120x + 22 = (300x + 25)/2

   240x + 44 = 300x + 25

   300x - 240 x = 44 - 25

   60x = 19

   x = 19/60

➛ Hence the normal time taken by the train to reach the destination is 19/60 hours or 19 mins.

➛ Substitute the value of x in equation 2,

    Distance = (300 x + 25)/6

    Distance = (300 × 19/60 + 25)/6

    Distance = (95 + 25)/6

    Distance = 20 km

➛ Hence the distance to be covered is 20 km.

   $\boxed{\bold{Distance\:to\:be\:covered=20\:km}}$

   

Answer 2

$\huge\mathtt\purple{\boxed{\underline\red{\overbrace\green{Question}}}}$

If a train runs at 40 kmph it reaches its destination late by 11 minutes but if it runs at 50 km pH it is late by 5 minutes only find the distance to be covered by the train.

$\huge\underbrace\mathfrak\red{Answer}$

$\huge\boxed{\fcolorbox{black}{pink{Distance \: 20 \: km}}$

${\bigstar}\large{\boxed{\sf{\pink{Given \: that}}}}$

• If a train run at a speed of 40 kilometre per hour it reaches the destination late by 11 minutes.
• If a train runs at a speed of 50 kilometre per hour it reaches the destination late by 5 minutes.

${\bigstar}\large{\boxed{\sf{\pink{To \: find}}}}$

• The distance to be covered by the train

${\bigstar}\large{\boxed{\sf{\pink{Solution}}}}$

• Let the time taken by the train to reach normally be x minutes'.

We know that,

⚫ Distance = Speed × Time

In first case,

If the train travel at the speed of 40 kilometre per hour it take 11 minute more than the normal time.

11 minutes = 11/60 hours

Hence,

Distance = 40 (x + 11/60)

Distance = 40 (60x + 11 /60)

Distance = (120x + 22) /3 Equation 1.

In second case,

If the train travel at the speed of kilometre per hour it takes 5 minute more than the normal speed.

5 minutes = 5/60 hours

Hence,

Distance = 50 (x+5/60)

Distance = 50 (60x + 5 ) /60

Distance = (300x +25/6) Equation 2.

Equating equations 1 and 2

(120x + 22) /3 = (300x +25/6)

120x + 22 = 300x + 25 / 2

240x + 44 = 300x + 25

300x - 240x = 44 - 25

60x = 19

x = 19/60

Hence, the normal time taken by the the train to reach the destination is 19/60 hours or 19 minutes

Substitute the value of x in equation 2

Distance = 300x + 25 /6

Distance = 300 × 19/60 +25 /6

Distance = 95 + 25 /6

Distance = 20 kilometre

Hope it's helpful

Thank you :)