Question

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Answer 1

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Answer 2

Let the Car at Place A be : A

Let the Car at Place B be : B

Given : Distance between the Places A and B : 80 km

Let the Speed of Car A be : P km/hr

Let the Speed of Car B be : Q km/hr

Given : If Both Cars start at the Same Time and Move in Same Direction, they meet in 8 Hours.

Let us Assume that Car B is moving towards its Right and Car A is moving towards its Right. It means Car be is Moving towards A.

✿ A ------------>                   ✿ B ------------>

We need to notice, One thing here that Distance travelled by the Car A in 8 Hours should be Equal to Distance travelled by Car B in 8 hours Plus Distance between the Two Places (i.e 80 km)

⇒ Distance travelled by Car A in 8 Hours = 8P

⇒ Distance travelled by Car B in 8 Hours = 8Q

⇒ 8P = 80 + 8Q

⇒ 8P - 8Q = 80 --------------- [1]

Given : If the Move towards each other, they meet in 1 Hour 20 Mins

We know that : One Hour 20 Mins $= (1 + \frac{1}{3}) = \frac{4}{3}\;Hour$

✿ A ----------->               <------------ B ✿

Here : The Distance travelled by Car A in Four - Third Hours and Distance travelled by Car B in Four - Third Hours should be Equal to 80 km

⇒ Distance travelled by Car A in Four Third Hours $= \frac{4}{3}(P)$

⇒ Distance travelled by Car B in Four Third Hours $= \frac{4}{3}(Q)$

$\bold{\implies \frac{4}{3}(P) + \frac{4}{3}(Q) = 80}$

$\bold{\implies P + Q = 60}$

Multiplying above Equation with 8, We get :

⇒ 8P + 8Q = 480 -------------- [2]

Adding Both Equation [1] and [2], We get :

⇒ (8P + 8Q) + (8P - 8Q) = 480 + 80

⇒ 16P = 560

⇒ P = 35

Substituting P = 35 in Equation P + Q = 60, We get :

⇒ 35 + Q = 60

⇒ Q = 60 - 35

⇒ Q = 25

⇒ The Speed of Car A at Place A is 35 km\hr

⇒ The Speed of Car B at Place B is 25 km\hr