Question

A train certain distance at a uniform speed If the train would have been 10km/hr faster,it would have taken 2 hours less than the schedule time and if the train were slower by 10 km/hr :it would have taken 3 hours more than the schedule time. find the distance covered by the train​

Answer 1

Answer:

Distance covered by the train​ = 600 km

Step-by-step explanation:

Let the speed of train be x km/hr and time taken be t hr.

So, Distance, D is given by = Speed * Time

             D   =  x * t ------ [Equation 1]

• First condition given is that if the train would have been 10 km/hr faster,it would have taken 2 hours less than the schedule time i.e.;

              D = (x + 10) * (t - 2)

              D = x * t - 2*x + 10*t - 20

               D = D - 2*x + 10*t - 20  {from equation 1}

                 10*t = 2*x + 20 --------- [Equation 2]

• Second condition given is that if the train were slower by 10 km/hr :it would have taken 3 hours more than the schedule time, i.e.;

                D = (x - 10) * (t + 3)

                D = x * t + 3*x - 10*t - 30

               D = D + 3*x - 10*t - 30  {from equation 1}

                 3*x - 10*t - 30 = 0 --------- [Equation 3]

Now putting value of 10*t from equation 2 into 3 we get,

              3*x - (2*x + 20) - 30 = 0

              3*x - 2*x - 50 = 0

                        x = 50 km/hr

putting value of x in equation 2 we get, t = $\frac{2*50 + 20}{10}$ = 12 hr

Therefore, D = x * t = 50 * 12 = 600 km .