(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
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.