Question

A train travels between two stations. The train will be on time if it runs at an average speed of 60 km/hour, but will be late by 5 minutes if it runs at an average speed of 50 km/hour. What is the distance between the two stations?

Answer 1

A train travels between two stations. The train will be on time if it runs at an average speed of 60 km/hour, but will be late by 5 minutes if it runs at an average speed of 50 km/hour. What is the distance between the two stations?

Solution:
           Let distance between stations(km) = x
                 let the time taken  (in hrs)when average speed is 60km/hr   = t
             then the time taken by train when average speed is  50 km/hr = t - 5minutes
                                                                                                       = (t - 1/60*5 )hrs
                                                                                                       = t-1/12
       Note :
                  60 minutes = one hour
                  1 minute = 1/60 hour
                   5 minutes = 5/60 hour
                   5 minutes = 1/12 hour
        we know that ,
                           average speed = total distance / total time taken
                       therefore ,
                               according to question ,
                                   60 = d / t.............(Given )
                         or        t = d/60
                               50 = d/ t-1/12    ........ (given)
                               substitute t in the above equation,
                           50 = d/ d/60 - 1/12
                       By Cross Multiplication , we get
                            50 (d/60  - 1/ 12) = d
                           50*d/60 - 50*1/12 = d
                           5/6 d - 50 /12 = d
                             5/6d -d = 50/12
                           5d - 6d/6 = 50/12
                         -d/6 = 50 /12
                     or -d = 50/12 *6
                     or -d = 50/2
                   or -d = 25
Ignoring negative sign ,because distance cannot be negative

                     d= 25 km
 
Hope this helps you!!

Answer 2

LET THE DISTANCE BETWEEN 2 STATION BE X
LET TIME TAKEN WHEN AVERAGE SPEED IS 60KM/HR=T
THEN TIME TAKEN WHEN AVERAGE SPEED IS 50KM/HR=T-5 MINUTES
                                                                               =(T-1/60*5)HRS
                                                                               =T-1/12
AVERAGE SPEED =TOTAL DISTANCE/TOTAL TIME TAKEN
GIVEN:
60=D/T
50=D/T-1/12
50=D/D/60-50*1/12=D
50*D/60-50*1/12=D
5/6D-50/12=D
5/6-D=50/12
5D-6D/6=50/12
-D/6=50/12
OR, -D=50/12*6
OR, -D=50/2
OR, -D=25
= -25
AS DISTANCE CANT BE WRITTEN AS NEGATIVE,
SO,IT IS 25 KILOMETER
HOPE THIS HELPS......