Question

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Answer 1

Q) Point A and B are 70 km a part on a highway. A car start from A and another car starts from B simultaneously .If they travel in the same direction they meet in 7 hours but if they travel towards each other , they meet in one hour. Find the speed of two cars.

$\rule{200}{2}$

=>Let the speed of car A be x kilometers per hour and speed of car B be y kilometers per hour.

CASE 1 :-

They Travel in same direction.

They meet After 7 hours.

Distance Travelled by car A = 7x

Distance travelled by car B = 7y

And,

Distance travelled by carA - Distance travelled by car B = 70 km

Thus,

7x-7y = 70

x - y = 10..... (i)

$\rule{200}{2}$

CASE 2:-

They travel in opposite direction.

they meet in one hour.

Distance travelled by car A = x

Distance travelled by car B = y

And,

Distance travelled by car A + distance travelled by car B = 70 km

Thus,

x + y = 70...... (ii)

$\rule{200}{2}$

Solving the two equations as follows :-

$x + y = 70 \\ \\ x - y = 10 \\ \\ = = = = = = = = = \\ \\ 2x = 80 \\ \\x = \frac{80}{2} \\ \\x = 40kmph$

$\rule{200}{2}$

Obtaining value of y :-

$x + y = 70 \\ \\y = 70 - x \\ \\ \\y = 70 - 40 \\ \\ y = 30kmph$

$\rule{200}{2}$

Hence,

Speed of car A = 40 kmph

Speed of car B = 30 kmph

$\rule{200}{2}$

Answer 2

As per given, let distance between A and B is 70 km [See diagram]

• When they travel in same direction, let them meet at "q" after 7hrs

• When they travel towards each other, let them meet at "p" in 1 hr.

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Solution

➵ AB = Aq - Bq

[Total d = d by A - d by B]

Let speed of A be "x" and B be "y".

➵ 70 = 7x - 7y

[Distance = Speed × Time]

➵ 10 = x - y ___(1)

______________________________

➵ AB = Ap + Bp

➵ 70 = 1x + 1y

➵ 70 = x + y ___(2)

On adding (1) and (2) we get,

➵ 80 = 2x

➵ 40 km/h = x (Speed of A)

By substituting value we get,

➵ 70 = 40 + y

➵ 30 km/h = y (Speed of B)

______________________________

1.1st Car speed 40 km/h

2. 2nd Car speed 30 km/h