Question

a train covered a certain distance at a uniform speed.if the speed of the train would have been 15 km/h more it would have taken 1.2 hours less than the scheduled time if the speed of the train would have been 12 km/h less. it would have 1.5 hours more than the scheduled time. find the distance covered by the train

Answer 1

Let x be speed of train and y be time taken
distance = xy
xy=(x+5)(y-1.2)
xy=xy-1.2x+15y-18
1.2x-15y+18=0
12x-150y+180=0
÷3
4x-50y+60=0
÷2
2x-25y+30=0___(1)
xy=(x-12)(y+1.5)
xy=xy+1.5x-12y-18
1.5x-12y-18=0
15x-120y-180=0
÷3
5x-40y-60=0
÷5
x-8y-12=0
*2
2x-16y-24=0____(2)
(1)-(2) = -9y+54=0
9y=54
y=54/9=6
therefore time= 6hrs
put y=6 in (1)
2x-25*6+30=0
2x-150+30=0
2x=120
x=120/2=60
therfore speed = 60km/hr
distance= xy
= 60*6
= 360km