two points A and B on a highway are at a distance of 240 km from each other the - Maths - Pair of Linear Equations in Two Variables

Question

two points A and B on a highway are at a distance of 240 km from
each other the car which startsfrom A moves with a constant speed
along the direction AB and the second car moves from B at thesame
time with a constant speed in the same direction the first car
overtakes the secondcar in four hours however the second car moves
from Btowards A then the car meet each other after 2 years finf the
speed of the car which starts fromB

Ajanta Trivedi · Accepted Answer

let the speed of the car which starts from point A be x km/hr and

the speed of the car which starts from point B be y km/hr

distance AB = 240 km.

if both the cars move in same direction AB, the first car overtakes the second car in 4 hrs.

therefore distance covered by first car in 4 hrs is 240 km more to the distance covered by second car .

distance = speed * time

$4 x = 4 y + 240 4 x - 4 y = 240 x - y = 60............... (1)$

if they move towards each other , they meet in 2 hrs.

therefore distance covered by first car and second car in 2 hrs is equal to 240 km

$2 x + 2 y = 240 x + y = 120............. (2)$

subtracting eq(1) from eq(2):

$2 y = 120 - 60 2 y = 60 y = \frac{60}{2} = 30 k m / h r$

thus the speed of the car which starts from B is 30 km/hr

hope this helps you.

cheers!!