CBSE Class 10 Answered
A TRAIN TRAVELS 360KM AT A UNIFORM SPEED.IF THE SPEED HAD BEEN 5KM/H MORE IT WOULD HAVE TAKEN 1HOUR LESS FOR THE SAME JOURNEY. FIND THE SPEED OF TH TRAIN
Asked by AVNI KHURANA | 24 Mar, 2013, 12:10: PM
Expert Answer
Let the speed = x km/h. Distance = 360km
then time taken = distance/speed
t1=360/x
if speed is increased by 5 km/h
speed will be (x+5)km/h
and distance is the same
t2= 360/(x+5)
time with original speed - time with increased speed = 1
t2= 360/(x+5)
time with original speed - time with increased speed = 1
i.e. t1 -t2 = 1
360/x - 360/(x+5)=1
LCM= x(x+5)
(360(x+5)-360x) /x(x+5)=1
360x+1800-360x=x(x+5)
x^2+5x = 1800
x^2+5x-1800=0
x^2+45x-40x-1800=0
x(x+45)-40(x+45)=0
(x-40)(x+45)=0
x= 40 km/h will be the original speed. (since, speed can't be negative and hence, can't be equal to -45km/h)
360/x - 360/(x+5)=1
LCM= x(x+5)
(360(x+5)-360x) /x(x+5)=1
360x+1800-360x=x(x+5)
x^2+5x = 1800
x^2+5x-1800=0
x^2+45x-40x-1800=0
x(x+45)-40(x+45)=0
(x-40)(x+45)=0
x= 40 km/h will be the original speed. (since, speed can't be negative and hence, can't be equal to -45km/h)
Answered by | 24 Mar, 2013, 09:11: PM
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