Math, asked by pastamkrishna, 9 months ago

(please answer to this question) A man travels by train and car to reach his office. If he travels by car for 10 km and the remaining by train, he reaches office in t hours. Doing exactly the opposite, he reaches office in (t + 0.5) hours. If the speeds of the train and the car are 50 km/h and 40 km/h, respectively, find the distance he travels to reach his office? ans =120 km. please explain step by step​

Answers

Answered by abhiappujari
8

Let the distance to the office be x.

Case I: distance by car = 10 km

           so, distance by train will be = x - 10 km

           time = t hrs

  We know that, speed = distance/time

  for train,           50= (x - 10)/ t'         [ t' is the time taken by the train]

  for car,              40= 10/t"                [t" is the time taken by car]

=>  total time of the journey is t (given) i.e  t = t" + t'   [total time will be equal to the sum of the time taken by both vehicle]

=>  putting the values of t' and t".

=>  t = 10/40 + (x-10)/50    ------------- (i)

Case II: distance by car = x - 10 km

            so, distance by train will be =  10 km

            time = t + 0.5 hrs  

  We know that, speed = distance/time

  for train,           50= 10/ t'         [ t' is the time taken by the train]

  for car,              40= (x-10)/t"                [t" is the time taken by car]

=>  total time of the journey is t (given) i.e  t = t" + t'   [total time will be equal to the sum of the time taken by both vehicle]

=>  putting the values of t' and t".

=>  t + 0.5 = 10/50 + (x-10)/40   ------------- (ii)

From eqn (i) and (ii) we can put the value of t

=> 10/40 + (x-10)/50 + 0.5 = 10/50 + (x-10)/40

[After solving this you will get x=120 km]

=> x = 120 km

So the distance to the office is 120 km.

 

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