Places A and B are 80 km apart on a highway. A car starts from A and another from B at the same
time If the cars travel in the same direction at different speeds, they meet in 5 hrs If they travel
towards each other, they meet in 1 hr. What are the speeds of the two cars?
Answers
Let the speed of car A be x km/hr and speed of car B be y km/hr.
Car A and B starts from same direction at different speed and they meet in
5 hrs, if they are 80 m apart from each other.
According to question,
=> 5x - 5y = 80
=> x - y = 16
=> x = 16 + y _____ (eq 1)
Car A and B meet in 1 hr. if they travel towrds each other.
According to question,
=> x + y = 80
=> 16 + y + y = 80 [From (eq 1)]
=> 2y = 80 - 16
=> 2y= 64
=> y = 32
Put value of y in (eq 1)
=> x = 16 + 32
=> x = 48
∴ Speed of car A is 48 km/hr and speed of car B is 32 km/hr.
ANSWER:-
Given:
Places A and B are 80km apart form each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 5 hours and if they move in opposite directions, they meet in 1hr.
To find:
The speeds of the cars.
Solution:
⏺️Let x & y be two cars starting from points A & B respectively.
⏺️Let the the speed of the car X be x km/hr and that of the car Y be y km/hr.
Case1:
When two cars move in the same directions:
Assume two cars meet at point Q, then;
Distance travelled by car X= AQ
Distance travelled by car Y= BQ
It is given that two cars meet in 5 hours
Distance travelled by car X in 8 hours
=) 5x km.
⏺️AQ= 5x
Distance travelled by car Y in 5 hours
=) 5y km
⏺️BQ= 5y
Clearly,
AQ- BQ= AB
=) 5x - 5y= 80
=) x - y= 16..............(1)
Case2:
When two cars move in opposite direction.
Suppose two cars meet at point P.
Distance travelled by X car X= AP
Distance travelled by Y car Y= BP.
In this case, two cars in 1 hours,
Therefore,
Distance travelled by car X in 1 hours
=) x km
Distance travelled by car Y in 1 hours
=) y km
So,
AP + BP =AB
=) x + y= 80..............(2)
By solving equation (1) & (2), we get;
x-y=16
x+y=80
________
2x = 96
=) x=96/2
=) x= 48
Therefore,
Substituting x =48 in equation (2), we get;
x + y= 80
=) 48 +y= 80
=) y= 80-48
=) y= 32
Hence,
⏺️Speed of car X is 48km/hr.
⏺️Speed of car Y is 32km/hr.