Answer :
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!!
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!!
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......
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......