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A fast train takes 3 hours less thn a slow train for a journey of 600 km.If the speed of the slow train is 10 km/hr less than that of the fast train find the speed of the two trains.

let the speed of slow train = x km/hr.

and the speed of fast train =( x+10) km/hr


Now,

Time to cover 600 km by slow  train = 600/x hrs.
Time taken by fast train to cover 600 km = 600/(x+10) hrs


∴According to question,



 

∴the speed of slow train = x km/hr = 40 km/hr

and the speed of fast train =( x+10) km/hr= 40+10= 50 km/ hr

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 d = 600 km

(fast trainspeed = x +10

(slow train)speed = x

since , distance = speed x time

for fast train --

 600 = (x+10) x (y-3)

600 = xy -3x +10y -30 .......(1)

for slow train ---

600 = (x) x (y)

xy =600 ...........(2)

from (1) and (2),

600 = 600 - 3(600/y) +10y -30

0 = -1800/y +10y -30

0 = -1800 +10y2 -30y 

0 = -180 +y2 -3y

by splitting the middle term,

y2 -(15-12)y -180

y2 -15y +12y -180

y(y-15) +12(y-15)

(y-15) (y+12)

since , speed cannot be negative .

therefore y =15 km/hr and speed of fast train = 25 km/hr.

HOPE THIS HELPS...

  • 1

here it goes !
d = 600 km

(fast trainspeed = x +10

(slow train)speed = x

since , distance = speed x time

for fast train --

600 = (x+10) x (y-3)

600 = xy -3x +10y -30 .......(1)

for slow train ---

600 = (x) x (y)

xy =600 ...........(2)

from (1) and (2),

600 = 600 - 3(600/y) +10y -30

0 = -1800/y +10y -30

0 = -1800 +10y2 -30y

0 = -180 +y2 -3y

by splitting the middle term,

y2 -(15-12)y -180

y2 -15y +12y -180

y(y-15) +12(y-15)

(y-15) (y+12)

since , speed cannot be negative .

therefore y =15 km/hr and speed of fast train = 25 km/hr.

  • 1
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