Question

If a train runs at 40kmph it reaches its destination late by 11 minutes.But if it runs at 50kmph it is late by 5minutes only Find the distance to be covered by the train​

Answer 1

Answer:

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

Step-by-step explanation:

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

• If speed is 40 km/hr , diatance will be covered 11 mins or 11/60 hours late

• If speed is 50 km/hr, distance will be covered 5 minutes or 5/60 hours late

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

• Distance to be covered

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

➜Let the actual time be x

➜Let the actual speed to reach the destination o time be y

➜ Distance is given by,

    Distance = Speed × Time

    Distance = y × x = xy

➜ By first condition, distance travelled is given by,

   xy = 40 × ( (x + 11)/60 ) ------equation 1

➜ By second condition, distance travelled is given by  

    xy = 50 ×( ( x + 5 )/60)----------equation 2

➜ Subtract equation 1 from equation 2

   xy - xy = 50 ×( ( x + 5 )/60) - [40 × ( (x + 11)/60 )]  

   0 = 5 ( x+5)/6 - [4 ( x + 11 ) /6]

➜ Multiply by 6 on both sides    

   0 = 5 ( x + 5 ) - [ 4 ( x + 11 ) ]  

   0 = 5x + 25 - [ 4x + 44 ]    

   x = 44 - 25    

   x = 19

➜ Hence the actual time taken to complete the journey would be 19 minutes or 19/60 hours

➜ Substitute the value of x in equation 2

   19/60 y = 50 × 24/60

   19 y = 1200    

       y = 63.2 km/hr

➜ Distance to travel = xy              

     = 19/60 × 63.2                

     = 20 km

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

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

→ Speed is the distance travelled per unit time. It's S.I unit is m/s

→ Speed is a scalar quantity. That is it has only magnitude and no direction.

Answer 2

If a train runs at 40 km/hr, it reaches its destination late by 11 minutes, but if it runs at 50 km/hr, it is late by 5 minutes only. The correct time for the train to complete the journey is 

A

13 min

B

15 min

C

19 min

D

21 min

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ANSWER

Let  the correct time for the train to complete the journey is x minuets

Then train cover distance in x+11 minuets at speed 40 km\hr =6040(x+11)km

Then train cover distance in x+5 minuets at speed 50 km\hr =6050(x+5)km

Both are same then 6040(x+11)=6050(x+5)

∴40x+440=50x+250

∴−10x=−190

∴x=19 minutes

Given :

Speed of train is \display \text{40 km/hr}\display40 km/hr and its late by 11 min or \displaystyle{\dfrac{11}{60} \ \text{hr}}6011 hr .

In other case it's also given speed of train is \display \text{50 km/hr}\display50 km/hr and late by 5 min or \displaystyle{\dfrac{5}{60} \ \text{hr}}605 hr .

Let the train covered 'd' km distance.

The journey let it took 't' hr time.

We have difference in late of time i.e.

\displaystyle{\dfrac{11}{60} -\dfrac{5}{60}=\dfrac{1}{10}}6011−605=101

We know ,

\display \text{Time = $\dfrac{\text{Distance}}{\text{Speed}}$}\displayTime = SpeedDistance

A.T.Q.

\begin{gathered}\displaystyle{\frac{\text{d}}{40} -\frac{\text{d}}{50}= \frac{1}{10}}\\\\\\\displaystyle{\dfrac{\text{d}}{10}(\frac{1}{4} -\frac{1}{5})= \frac{1}{10}}\\\\\\\displaystyle{\text{d}(\dfrac{1}{20})=1}\\\\\\\displaystyle{\text{d}=20 \ \text{km}}\end{gathered}40d−50d=10110d(41−51)=101d(201)=1d=20 km

Hence , the distance to be covered by the train is 20 km .