# A man travels 600km partly by train and partly by car. If he covers 400km by train and the rest by car, it takes him 6 hours and 30 minutes. But if he travels 200 km by train and rest by car, he takes half an hour longer. Fine the speed of the train and that of the car

Let x = speed of train

Let y = speed of car

speed = distance / time
time = distance / speed

6 hours 30 minutes = 6.5 hours <== 400 km by train ; 200 km by car
1/2 hour longer = 7 hours <== 200 km by train ; 400 km by car

Train time + car time = total time

400 / x + 200 / y = 6.5 <== two equations and two unknowns
200 / x + 400 / y = 7 . . . . . . solve for x and y

400y + 200x = 6.5 xy
200y + 400x = 7 xy

400y - 6.5 xy = - 200x
200y - 7xy = - 400x

y ( 400 - 6.5x) = -200x
y ( 200 - 7x) = -400x

y (6.5x - 400) = 200x
y (7x - 200) = 400x

y = 200x / (6.5x - 400)
y = 400x / (7x - 200) *

. . . since both equal y, the difference is zero

200x / (6.5x - 400) - 400x / (7x - 200) = 0

200x ( 7x - 200) - 400x (6.5x - 400) = 0

1400x^2 - 40000x - 2600x^2 + 160000x = 0

120000 x - 1200 x^2 = 0

100 - x = 0

x = 100 km / h = train speed

y = 400x / (7x - 200) . from *

y = 400 * 100 / (7 * 100 - 200)

y = 80 km / h = car speed

• 44

hope this helped !!

• -4

Let the speed of train be x km/hr and that of the train be y km/hr.

So, .......(1)

Similarly ......(2)

Multiply equation (1) by 2 to get, .....(3)

Subtracting equation 2 from 3 So speed of train is 100 km/h and car is 80 km/h.

• 13
Let speed of train be x km/hr and car be y km/hr
Total distance=600km
CASE 1
Distance travelled by train=400km
Distance travelled by car  =600-400=200km
Time taken by train = D/S=400/x
Time taken by car   = D/S=200/y
CASE 2
Distance travelled by train=200km
Distance travelled by car  =600-200=400km
Time taken by train = D/S=200/x
Time taken by car   = D/S=400/y
A.T.Q
400 200 = 6+30
x        y          60
Let 1/x and 1/y be a and b
400a+200b=13/2
200a+100b=13/4..........(i)
AND
2004007
x        y
Let 1/x and 1/y be a and b
200a+400b=7......(ii)
In (i) & (ii)using elimination method
200a+100b=13/4
+200a+400b=+7
-         -            -
-300b=-15/4
b=-15/4*-300
b=1/80
and Putting in (ii) we get
200a=7-400(1/80)
a=2/200
a=1/100
NOW a=1/x and b=1/y
so x=>Speed of train=>100 km/hr
and y=>Speed of car=>80km/hr

• 29
200a + 100b =13/4. May I know how you got 13/4?
• -8
for such questions
you can subscribe to channel "kamal bajaj aptitude"   a good trick is given for this question

• -12
total dist to travel = 600 km
we need to find the speed so speed = dist/time ( d=s/t)
let the speed of train be x kmph and bus be y kmph
first case
train 400 km
bus 200km
time 13/2 hours

400/x + 200/y = 13/2

second case
train = 200 km
car 400 km
time = 7 hours

200/x + 400/y = 7
let 1/x be u and 1/y be v
400u+200v=13/2 or 800u+400v=13
200u+400v=7
solve them
x = train = 100kmph
y= car=80kmph
• 65
not understand

• -4
Let x = speed of train Let y = speed of car speed = distance / time time = distance / speed 6 hours 30 minutes = 6.5 hours <== 400 km by train ; 200 km by car 1/2 hour longer = 7 hours <== 200 km by train ; 400 km by car Train time + car time = total time 400 / x + 200 / y = 6.5 <== two equations and two unknowns 200 / x + 400 / y = 7 . . . . . . solve for x and y 400y + 200x = 6.5 xy 200y + 400x = 7 xy 400y - 6.5 xy = - 200x 200y - 7xy = - 400x y ( 400 - 6.5x) = -200x y ( 200 - 7x) = -400x y (6.5x - 400) = 200x y (7x - 200) = 400x y = 200x / (6.5x - 400) y = 400x / (7x - 200) *  . . . since both equal y, the difference is zero
• 4
Speed of train = 100 km/h
Speed  of  car =  80 km/h
• -7
Speed of train=100 km/h
Speed of car=80 km/h
• 3
Let X and y km/h
• -2
Let x=train speed
Let y = car speed

speed = distance / time
time = distance / speed

6 hours 30 minutes = 6.5 hours <== 400 km by train ; 200 km by car
1/2 hour longer = 7 hours <== 200 km by train ; 400 km by car

Train time + car time = total time

400 / x + 200 / y = 6.5 <== two equations and two unknowns
200 / x + 400 / y = 7 . . . . . . solve for x and y

400y + 200x = 6.5 xy
200y + 400x = 7 xy

400y - 6.5 xy = - 200x
200y - 7xy = - 400x

y ( 400 - 6.5x) = -200x
y ( 200 - 7x) = -400x

y (6.5x - 400) = 200x
y (7x - 200) = 400x

y = 200x / (6.5x - 400)
y = 400x / (7x - 200) . . . note this equation ... for later use

. . . since both equal y, the difference is zero

200x / (6.5x - 400) - 400x / (7x - 200) = 0

200x ( 7x - 200) - 400x (6.5x - 400) = 0

1400x^2 - 40000x - 2600x^2 + 160000x = 0

120000 x - 1200 x^2 = 0

100 - x = 0

x = 100 km / h <===== train speed

y = 400x / (7x - 200) . . . see note above

y = 400 * 100 / (7 * 100 - 200)

y = 80 km / h <===== car speed

hope it helped  u
• 4
Let x=train speed
Let y = car speed

speed = distance / time
time = distance / speed

6 hours 30 minutes = 6.5 hours <== 400 km by train ; 200 km by car
1/2 hour longer = 7 hours <== 200 km by train ; 400 km by car

Train time + car time = total time

400 / x + 200 / y = 6.5 <== two equations and two unknowns
200 / x + 400 / y = 7 . . . . . . solve for x and y

400y + 200x = 6.5 xy
200y + 400x = 7 xy

400y - 6.5 xy = - 200x
200y - 7xy = - 400x

y ( 400 - 6.5x) = -200x
y ( 200 - 7x) = -400x

y (6.5x - 400) = 200x
y (7x - 200) = 400x

y = 200x / (6.5x - 400)
y = 400x / (7x - 200) . . . note this equation ... for later use

. . . since both equal y, the difference is zero

200x / (6.5x - 400) - 400x / (7x - 200) = 0

200x ( 7x - 200) - 400x (6.5x - 400) = 0

1400x^2 - 40000x - 2600x^2 + 160000x = 0

120000 x - 1200 x^2 = 0

100 - x = 0

x = 100 km / h <===== train speed

y = 400x / (7x - 200) . . . see note above

y = 400 * 100 / (7 * 100 - 200)

y = 80 km / h <===== car speed

hope it helped  u
• 3
Can u plz solve dis by graphical method...
• -3
Can u plz solve this by graphical method.... Actually I want that...
• 0
Train-x 100 km /h and car -y 80km/h
• -1
Let x = speed of train Let y = speed of car  speed = distance / time time = distance / speed 6 hours 30 minutes = 6.5 hours
• -1
total distance man travels= 600 km
CASE 1; he travels 400 km by train and 200 km by car
CASE 2; he travels 200 km by train and 400 km by car
let the speed of train = x kmph
let the speed of car = y kmph
400/x + 200/y=13/2
200/x + 400/y= 7
let 1/x = a  , 1/y= b
400a + 200b =13/2           800a + 400b = 13 ----------(1)
200a + 400b = 7  ------------(2)

subtracting (1) and (2)
600a=6
a=1/100
substituiting the value of a in (2)
b=1/80

so,
the speed of train is 100 kmph
the speed of car is 80 kmph
• -1
guy don t confused is easy very easy

• 0
very very hot sum
• 2
A man travels 600 kms partly by train and partly by car. It takes 8 hrs and 40 mins if he travels 320 kms by train and rest by car. It would take 30 mins more if he travels 200 kms by train and the rest by car. Find the speed of the train and the car separately.
• 0
The speed of train is 100 km/hr The speed of car is 80 km/hr
• 0
Let x=train speed Let y = car speed  speed = distance / time  time = distance / speed  6 hours 30 minutes = 6.5 hours
• 3
total dist to travel = 600 km we need to find the speed so speed = dist/time ( d=s/t) let the speed of train be x kmph and bus be y kmph first case train 400 km bus 200km time 13/2 hours 400/x + 200/y = 13/2 second case train = 200 km car 400 km time = 7 hours 200/x + 400/y = 7 let 1/x be u and 1/y be v 400u+200v=13/2 or 800u+400v=13 200u+400v=7 solve them x = train = 100kmph y= car=80kmph
• 3
Let x=train speed
Let y = car speed

speed = distance / time
time = distance / speed

6 hours 30 minutes = 6.5 hours <== 400 km by train ; 200 km by car
1/2 hour longer = 7 hours <== 200 km by train ; 400 km by car

Train time + car time = total time

400 / x + 200 / y = 6.5 <== two equations and two unknowns
200 / x + 400 / y = 7 . . . . . . solve for x and y

400y + 200x = 6.5 xy
200y + 400x = 7 xy

400y - 6.5 xy = - 200x
200y - 7xy = - 400x

y ( 400 - 6.5x) = -200x
y ( 200 - 7x) = -400x

y (6.5x - 400) = 200x
y (7x - 200) = 400x

y = 200x / (6.5x - 400)
y = 400x / (7x - 200) . . . note this equation ... for later use

. . . since both equal y, the difference is zero

200x / (6.5x - 400) - 400x / (7x - 200) = 0

200x ( 7x - 200) - 400x (6.5x - 400) = 0

1400x^2 - 40000x - 2600x^2 + 160000x = 0

120000 x - 1200 x^2 = 0

100 - x = 0

x = 100 km / h <===== train speed

y = 400x / (7x - 200) . . . see note above

y = 400 * 100 / (7 * 100 - 200)

y = 80 km / h <===== car speed
hope i helped u:)

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