Question

Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in same direction they meet in 8hours and if they move towards each other they meet in 1h 20minutes. Find speed of the cars​

Answer 1

Step-by-step explanation:

Let,

The speed of car at A be x km/h

The speed of car at B be y km/h

First we need to derive equations

Case I,

According to question when they move in same direction

=> 8x - 8y = 80

=> x - y = 10

=> x = 10 + y.........(ii)

Case II,

According to question when they move towards each other

=> 4x/3x + 4y/3 = 80

=> 4x + 4y/3 = 80

=> 4x + 4 y = 240

=> x + y = 60........(ii)

Now by help of equation (i) and equation (ii) we can find value of x and y

Now,

Put the value of x in equation (ii)

=> 10 + y + y = 60

=> 10 + 2y = 60

=> 2y = 60 - 10

=> 2y = 50

=> y = 50/2

=> y = 25km/h

Now, put the value of y in any of the equation to get value of x

=> x = y + 10

=> x = 25 + 10

=> x = 35km/h

Hence,

Speed of cars at A is 35km/h and at B is 25 km/h.

Used Concept-

1. Always remember when any object is in same direction then we need to find Difference of speeds.

2. But when they are in opposite direction speed will be added.

Answer 2

let velocity of A be x and B be y

when they are moving in same direction, their velocities will add up

=> 80/(x+y)=80(in min)

and when they move in same direction, their net velocity will be considered as their difference.

=> 80/(x-y)=480(in min)

=>x= 35 km/hr and y=25 km/hr

i hope this will help you!!!!