Login/Sign Up
Home » Places A and B are apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in and if they move in opposite directions, they meet in . Find the speeds of the cars.
Places A and B are 80km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in 8hr and if they move in opposite directions, they meet in 1hr20min. Find the speeds of the cars.
CBSE | Class 10 | Exercise 3.10 | Maths | Pair of Linear Equations In Two Variables | RD Sharma
Places A and B are 80km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in 8hr and if they move in opposite directions, they meet in 1hr20min. Find the speeds of the cars.

Let the speed of the car leaving A to be ‘x’ km/h and the speed of the car leaving B to be ‘y’ km/h.

Total distance=80 km

Also 1 hour 20 mins= 4/3 hour

When an automobile goes in the same direction as a specified condition,

Distance travelled by y= 8y km

Distance travelled by x= 8x= 80+8y

Now, Equation formed is 8x=80+8y

\Rightarrow 8x-8y=80

\Rightarrow x-y=10 —-(1)

Similarly, For opposite direction,

Distance travelled by x= (4/3)x

Distance travelled by y= (4/3) y

Also total distance covered= 4/3 \times x+4/3y

\Rightarrow 80= 4x+4y/3

\Rightarrow 240= 4x+4y

\Rightarrow 60=x+y —-(2)

Solving Equation (1) and (2)

\Rightarrow 60=x+y —-(2)

\Rightarrow x-y=10 —-(1)

\Rightarrow x= 10+y —-(3)

Substituting the value of (3) in (2) we get,

\Rightarrow 60= 10+y+y

\Rightarrow 60-10=2y

\Rightarrow 50=2y

\Rightarrow 25=y

Also we know that, x=10+y=> x= 10+25=> x=35

Thus, Speed of car starting from A is 35km/h

Speed of car starting from B is 25km/h

i

More Material