Question

Suppose a car starts from a place A and travels at a speed of 40 Km/h towards another place B. At the same time another car starts from B and
travels towards A at a speed of 30 Km/h. If the distance between A and B is 100 km; after how much time will that cars meet?​

Answer 1

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Here we are given

A car starts from 'A' with a speed of 49 kmph and travelling towards B.

Another car starts from B and is travelling towards A with a speed of 30 kmph.

Distance between A and B is 100 km.

$\huge{\orange{\underline{\red{\mathtt{Mathematical}}}}}$

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Here we use the formula T = D/S

T - The time after the toe cars meet

D - Total distance to be travelled by the 2 cars together

S - Relative speed of the cars.

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Speed of the first car = 40 kmph

Speed of the second car = 30 kmph

'S' - Relative speed (i.e.,) the total distance travelled by two cars in one hour = 40+30=70kmph

D = 100 km

T = D/S = 100/60 = 10/7 = $1 \times \frac{3}{7}$Hrs.

$\huge{\orange{\underline{\red{\mathtt{Interpretation :-}}}}}$

Here, T = $1 \times \frac{3}{7}$ Hrs.

This means the two cars meet after $1 \times \frac{3}{7}$ Hrs.

$\huge{\orange{\underline{\red{\mathtt{Validation :-}}}}}$

In the given problem, we assume that cars are travelling with constant speeds. If the speed changes, our model T = D/S will not work. We are also assuming that the cars travel without shopping at any point.

Answer 2

Answer:

Let speed of car starting from A=x km/hr and speed of car starting from B=y km/hr.

Relative speed of A with respect to B when moving in same direction =x−y km/hr.

Relative speed of A with respect to B when moving in opposite direction =x+y km/hr.

Distance between A and B=100 km.

We know, Time=

Speed

Distance

From the above information, we have,

x−y

100

=5and

x+y

100

=1

or,

x−y

100

=5

=>100=5(x−y)

=>20=x−y

=>x=y+20....(i)

Also,

x+y

100

=1

=>100=x+y

=>x+y=100....(ii)

By substitution method,

Substituting equation (i) in equation (ii), we get,

x+y=100

=>y+20+y=100

=>2y=80

=>y=40

Substituting y=40 in equation (i), we get,

x=y+20

=>x=40+20

=>x=60

Thus, speed of car starting from A=x=60 km/hr and speed of car starting from B=y=40 km/hr.