Point A and B are 70 km apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours. But if the travel towards each other, they meet in one hour. Find the speed of the two cars.
Answers
SOLUTION :
Let X and Y be two cars starting from points A and B . Let the speed of car X be x km/hr and that of car Y be y km/hr.
Case 1 :
When both cars move in the same directions:
Let two cars meet at point Q, Then,
Distance travelled by car X = AQ
Distance travelled by car Y = BQ
Given : Both cars meet in 7 hours.
Therefore, In 7 hours ,distance travelled by car X = 7x km
AQ =7 x
In 7 hours,distance traveled by car Y in 7 hours = 7y km
BQ= 7y
AQ - BQ = AB
7 x - 7 y = 70
[AB = 70 km]
7(x - y ) = 70
x - y = 70/7
x - y = 10………………….(1)
Case II :
When two cars move in opposite direction
Let two cars meet at point P.Then,
Distance travelled by car X = AP ,
Distance travelled by car Y = BP,
Given : Two cars meet in 1 hour
Therefore ,Distance travelled by car X in 1 hour =1x km
AP =x
Distance travelled by car Y in 1 hour = y km
BP= y
AP+BP= AB
x+ y=70 …………….…(2)
On Adding equation (i) and (ii),
x - y = 10
x+ y=70
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2x = 80
x = 80/2
x = 40
On Putting x = 40 in equation (2) we get
x + y = 70
40+y =70
y = 70 - 40
y =30
Hence, the speed of car X starting from point A is 40km/h and the speed of car Y starting from point B is 30 km/hr.
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