Question

14. Places A and B are 100 km apart on a highway. One car starts from A and another from 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. What are the speeds of the two cars? While
driving, the driver should maintain the speed limit as allowed Comment.

Standard:- 10

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Answer 1

Sol:
Let the speeds of the cars be x km/hr and y km/hr

Case 1:
When the cars are going in the same direction
Relative speed = x - y
Distance = 100 km
Time = 100 / (x - y) = 5 hrs
x - y = 100 / 5=20
x – y = 20 ------------- (1)

Case 2:
When the cars are going in the opposite direction
Relative speed = x + y
Time =100 / (x + y) = 1 hrs
x + y = 100 ------------- (2)

Solving the equations (1) and (2),
x = 60
y = 40
Hence the speeds of the cars are 60 km/hr and 40 km/hr.

Answer 2

Heya !!!



Let the speed of car at A be X km/hr


And,


Speed of car at B be Y km/hr



According to question,


5X - 5Y = 100


5 ( X - Y ) = 100


X - Y = 100/5


X - Y = 20 -------(1)


And,


X + Y = 100 --------(2)



From equation (1) we get,

X - Y = 20

X = (20+Y) -----(3)


Putting the value of X in equation (2)


X + Y = 100

20 + Y + Y = 100

2Y = 100-20

2Y = 80

Y = 80/2

Y = 40 km/hr


Putting Y = 40 in equation (3)


X = 20 + Y

X = 20+40 = 60 km/hr


Therefore,


Speed of Car at A = 60 kmph

And,


Speed of Car at B = 40 kmph.



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