Places A and B are 100 km apart on a highway. One car starts form A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of two cars?
Answers
Step-by-step explanation:
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Given : Places A and B are 100 km apart on a highway. One car starts form A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour.
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 5 hours.
Therefore, In 5 hours ,distance travelled by car X = 5x km
AQ = 5 x
In 5 hours,distance traveled by car Y in 5 hours = 5y km
BQ = 5y
AQ - BQ = AB
5x - 5y = 100
[AB = 100 km]
5(x - y ) = 100
x - y = 100/5
x - y = 20………………….(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 = 100 …………….…(2)
On adding equation (1) and (2) :
x - y = 20
x + y = 100
------------
2x = 120
x = 120/2
x = 60
On Putting x = 60 in equation (2) we get
x + y = 100
60 + y =100
y = 100 - 60
y = 40
Hence, the speed of car X starting from point A is 60km/h and the speed of car Y starting from point B is 40 km/hr.
Hope this answer will help you…
Some more questions from this chapter :
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.
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A and B are two points 150 km apart on a highway. Two cars start with different speeds from A and B at same time. If they move in same direction, they meet in 15 hours. If they move in opposite direction, they meet in one hour. Find their speeds.
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