# Places A and B are 100 km apart on a highway. One car starts from A and anotherfrom B at the same time. If the cars travel in the same direction at different speeds,they meet in 5 hours. If they travel towards each other, they meet in 1 hour. Whatare the speeds of the two cars?

LET THE SPEED OF 1 CAR BE X & OTHER BE Y

DIST COVERED BY A IN 5 HR. = 5 * X = 5X

DIST COVERED BY B IN 5 HR = 5Y

A/Q WHEN THEY TRAVEL IN SAME DIRECTION

THEN 5X - 5Y = 100 => X -Y =20 .....(!)

NOW, DIST COVERED BY A IN 1 HR = X

DIST COVERED BY B IN 1 HR = Y

WHEN THEY TRAVEL TOWARDS EACH OTHER

THEN

A/Q, X +Y =100 ......(2)

NOW (!) - (2) = ( X -Y)-( X +Y)=20 - 100

=> 2Y = 80 HENCE Y = 40 KM /HR.

AND X= 20 +Y = 60 KM/HR

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Catch-up DATA:A's DATA:rate = a km/hr ; time = 5 hrs; distance = 5a kmB's DATA:rate = b km/hr ; time = 5 hrs; distance = 5b kmNote If A catches up to B, A's distance is 100 km + 5bSo, 5a = 5b+100Meeting DATA:A's DATA:rate = a km/hr ; time = 1 hr; distance = a kmB's DATA:rate = b km/hr ; time = 1 hr; distance = b kmEquation:a+b = 100 kmSo you have two equations:5a = 5b+100a+b = 100Modifying those you get:a-b = 20a+b = 100Add and solve for "a:2a = 120a = 60 km/hr (A's rate)---Solve for "b":a + b = 10060 +b = 100b = 40 mph (B's rate)Cheers,

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Let speed of faster car = x Km/ h

Speed of slower car = y km /hRelative speed when both car travels in same direction = x - yIf the cars travel in the same direction at different speeds, they meet in 5 hoursSpeed = distance/ timeTotal distance= 100 kmSpeed x y = 100/5X y = 20Add y both side we getX = 20 + y(1)Relative speed when both car travels in opposite direction = x + yIf they travel towards each other, they meet in 1 hour.Speed = distance/ timeTotal distance= 100 kmSpeed x+ y = 100/1Plug the value of x form equation first we get20 + y + y = 1002y = 80Y = 40Plug the value of y in equation first we getX= 20 + 40X = 60
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the answer which is posted by vikash kr. is correct

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Yes
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solve the following system of equations graphically x+2y=5,2x-3y=-4.also find the points where the lines meet at x-axis
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thank you!!!
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Let the speed of car which starts from A be x and from B be y
Therefore,speed of car from A in 5 hours = 5 x
speed of car from B in 5 hours = 5 y
Case 1
Both the cars travel in the same direction,
Therefore, 5 x - 5 y =  100
5 (x - y) = 100
Thus , x -y = 100/5= 20
Also,  x = 20 + y . . . . . . . . (1)

Case 2
Both the cars travel in opposite direction,
Therefore, x + y = 100
From (1) , {20 + y} + y = 100
20 + 2 y = 100
2 y = 100 - 20
2 y = 80
Thus, y = 80/2 = 40 Km/hr
Substituting y = 40 in (1),
x = 20 + y
= 20 + 40
= 60 Km/hr

Thus, the speed of car which starts from A is 60 Km/hr and that of the car which starts from B is 40 Km/hr

HOPE IT HELPED YOU

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hence the speed of cars are 60 km per hour and 40 km per hour hope It helped cheers!!! • 24
2nd answer is easy to understand
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Hii gyz tmrw is my priodc test.....so tntion ...bt in prvs tst I got 40 out of 40 and evry 1 were failed except 3 included me....so give me bst of lk guz so that I can clear this xm also by securing full mrks
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LET THE SPEED OF 1 CAR BE X & OTHER BE Y

DIST COVERED BY A IN 5 HR. = 5 * X = 5X

DIST COVERED BY B IN 5 HR = 5Y

A/Q WHEN THEY TRAVEL IN SAME DIRECTION

THEN 5X - 5Y = 100 => X -Y =20 .....(!)

NOW, DIST COVERED BY A IN 1 HR = X

DIST COVERED BY B IN 1 HR = Y

WHEN THEY TRAVEL TOWARDS EACH OTHER

THEN

A/Q, X +Y =100 ......(2)

NOW (!) - (2) = ( X -Y)-( X +Y)=20 - 100

=> 2Y = 80 HENCE Y = 40 KM /HR.

AND X= 20 +Y = 60 KM/HR

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