# A train covered

Let the actual speed of the train be x km/hr and the actual time taken be y km/hr.
Then, Distance = Speed × Time taken = (xy) km
If the speed is increased by 6 km /hr, then time of journey is reduced by 4 hours.

When speed is (x + 6) km / hr, time of journey is (y – 4) hours.

Distance = (x + 6) (y – 4)

xy = xy - 4x + 6y – 24

-4x + 6y + 24 = 0

-2x + 3y - 12 = 0 … (i)
When the speed is reduced by 6 km/hr, then the time taken for the journey is increased by 6 hours.
When the speed is (x – 6) km/hr, time of journey is (y + 6) hours
Distance = (x – 6) (y + 6)
xy = (x – 6) (y + 6)
xy = xy + 6x – 6y – 36

6x – 6y – 36 = 0

x – y – 6 = 0… (ii)
Solving (i) and (ii),
Using cross multiplication, we have,

x = 30 and y = 24
Putting the values of x and y in equation (i) we get,
Distance = 30 × 24 = 720 km

The length of the journey = 720 km.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Introduction to Linear Equations in Two Variables62 mins
Pair of Linear Equations-Yahaan se laye marks57 mins
Revision on Substitution and Elimination Method44 mins
Revision on Word Problems - 150 mins
Revision on Word Problems - 235 mins
Resistors in Series33 mins
Steps in Reproduction43 mins
Resistors in Parallel36 mins
Electric Motor37 mins
Magnetic Field of Circular Conductor41 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Draw the graph ofNCERT - Mathematics