Question

Points A and B are 70km apart from each other on a highway . A car starts from A and another from B at the same time . If they go in the same direction they meet in 7 hours and if they go in opposite directions they meet in one hour . Find the speed of the two cars .

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, Speed of car starting from A is x km/h & speed of car starting from B is y km/h. ( where x > y .)

Case ❶ :- (Same Direction).

since Speed of car starting from A is more Than , starting from B , and they will meet in 7 hours.

So,

→ Usual Speed = (x - y) km/h.

→ Distance covered Before Meeting = 70km.

→ Time = 7 Hours.

Therefore,

→ Speed = (Distance/Time).

→ (x - y) = (70/7)

→ (x - y) = 10km/h. ------------ Eqn.(1).

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Case ❷ :- (Opposite Direction).

since Speed of car starting from A is more Than , starting from B , and they will meet in 1 hours.

So,

→ Usual Speed = (x + y) km/h.

→ Distance covered Before Meeting = 70km.

→ Time = 1 Hours.

Therefore,

→ Speed = (Distance/Time).

→ (x + y) = (70/1)

→ (x + y) = 70km/h. ------------ Eqn.(2).

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Adding Both Eqn's. Now, we get,

→ (x - y) + (x + y) = 10 + 70

→ x + x - y + y = 80

→ 2x = 80

→ x = 40 km/h. (Ans.)

Putting This value in Eqn.(1) Now, we get,

→ 40 - y = 10

→ y = 40 - 10

→ y = 30 km/h . (Ans.)

Hence, Speed of Train starting from A is 40km/h & Speed of Train starting from B is 30km/h...

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(Nice Question of Basic.).

Answer 2

Answer:

Given:

• Points A and B are 70 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in the same direction they meet in 7 hours and if they go in opposite directions they meet in one hour.

Find:

• Find the speed of the two cars.

Concept:

• Let us assume x,y as speed of A,B. The given question is divided in to two case. Talking about first part A and B starts form the same time. According to part two they are going in opposite directions. So, Let their speed be (x - y) as they move in the same time and let (x + y) be their speed when they move in opposite direction.

Case(1)

• Using formula:

☆ ${\sf{\underline{\boxed{\red{\sf{Speed = \dfrac{Distance \: covered}{Time \: taken}}}}}}}$

Calculations:

⇒ $\bold{(x - y) = (\dfrac{70}{7})}$

⇒ ${\sf{\underline{\boxed{\orange{\sf{(x - y) = 10 --- Equation(1)}}}}}}$

Case(2)

• Using formula:

☆ ${\sf{\underline{\boxed{\red{\sf{Speed = \dfrac{Distance \: covered}{Time \: taken}}}}}}}$

Calculations:

⇒ $\bold{(x + y) = (\dfrac{70}{1})}$

⇒ ${\sf{\underline{\boxed{\orange{\sf{(x + y) = 70 ---Equation (2)}}}}}}$

Adding Eq(1) with Eq(2); we get:

⇒ $\bold{(x - y) + (x + y) = 10 + 70}$

⇒ $\bold{x + x - y + y = 80}$

⇒ $\bold{2x = 80}$

⇒ ${\sf{\underline{\boxed{\green{\sf{x = 40 \:km/hr}}}}}}$

Therefore, 40 km/hr is the speed of Train starting from A.

Adding values in Eq(1); we get:

⇒ $\bold{40 - y = 10}$

⇒ $\bold{y = 40 - 10}$

⇒ ${\sf{\underline{\boxed{\green{\sf{y = 30 \: km/hr }}}}}}$

Therefore, 30 km/hr is the speed of Train starting from B.

HENCE, 40 km/hr and 30 km/hr are answers!!!