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Two Cars started at same time, same place and towards same direction. First Car goes at a speed of 5km/hr in first and 7 Km/hr in second hour and repeats the cycle over the entire journey. Similarly second Car goes at 4km/hr in first hour and 9km/hr in second hour and repeats the cycle over the entire journey.Then these two Cars for the first time for after how many hours of journey?
- a)3 Hours
- b)6 Hours
- c)9 Hours
- d)12 Hours
- e)None
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two Cars started at same time, same place and towards same direction. ...
First car : 5,12,17
Second Car: 4,3,17
Most Upvoted Answer
Two Cars started at same time, same place and towards same direction. ...
Solution:
Let us assume that the two cars meet after 'x' hours of journey.
Distance covered by the first car in 'x' hours = Distance covered by the second car in 'x' hours
Let us calculate the distance covered by both cars in the first cycle of 2 hours each.
Distance covered by the first car in the first cycle = 5 km/hr + 7 km/hr = 12 km
Distance covered by the second car in the first cycle = 4 km/hr + 9 km/hr = 13 km
Let us calculate the distance covered by both cars in the second cycle of 2 hours each.
Distance covered by the first car in the second cycle = 5 km/hr + 7 km/hr = 12 km
Distance covered by the second car in the second cycle = 4 km/hr + 9 km/hr = 13 km
The distance covered by both cars in each cycle is the same.
Let us assume that the two cars meet after 'x' hours of journey.
Distance covered by the first car in 'x' hours = Distance covered by the second car in 'x' hours
In the first 'x' hours, the first car covers 12 km in each cycle of 2 hours.
Therefore, the distance covered by the first car in 'x' hours = 12 * (x/2) km
In the first 'x' hours, the second car covers 13 km in each cycle of 2 hours.
Therefore, the distance covered by the second car in 'x' hours = 13 * (x/2) km
Equating the above two equations, we get:
12 * (x/2) = 13 * (x/2)
6x = 13x/2
x = 3 hours
Therefore, the two cars will meet for the first time after 3 hours of journey.
Hence, the correct answer is option 'A'.
Let us assume that the two cars meet after 'x' hours of journey.
Distance covered by the first car in 'x' hours = Distance covered by the second car in 'x' hours
Let us calculate the distance covered by both cars in the first cycle of 2 hours each.
Distance covered by the first car in the first cycle = 5 km/hr + 7 km/hr = 12 km
Distance covered by the second car in the first cycle = 4 km/hr + 9 km/hr = 13 km
Let us calculate the distance covered by both cars in the second cycle of 2 hours each.
Distance covered by the first car in the second cycle = 5 km/hr + 7 km/hr = 12 km
Distance covered by the second car in the second cycle = 4 km/hr + 9 km/hr = 13 km
The distance covered by both cars in each cycle is the same.
Let us assume that the two cars meet after 'x' hours of journey.
Distance covered by the first car in 'x' hours = Distance covered by the second car in 'x' hours
In the first 'x' hours, the first car covers 12 km in each cycle of 2 hours.
Therefore, the distance covered by the first car in 'x' hours = 12 * (x/2) km
In the first 'x' hours, the second car covers 13 km in each cycle of 2 hours.
Therefore, the distance covered by the second car in 'x' hours = 13 * (x/2) km
Equating the above two equations, we get:
12 * (x/2) = 13 * (x/2)
6x = 13x/2
x = 3 hours
Therefore, the two cars will meet for the first time after 3 hours of journey.
Hence, the correct answer is option 'A'.
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Community Answer
Two Cars started at same time, same place and towards same direction. ...
First car : 5,12,17
Second Car: 4,3,17
Second Car: 4,3,17
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Two Cars started at same time, same place and towards same direction. First Car goes at a speed of 5km/hr in first and 7 Km/hr in second hour and repeats the cycle over the entire journey. Similarly second Car goes at 4km/hr in first hour and 9km/hr in second hour and repeats the cycle over the entire journey.Then these two Cars for the first time for after how many hours of journey?a)3 Hoursb)6 Hoursc)9 Hoursd)12 Hourse)NoneCorrect answer is option 'A'. Can you explain this answer?
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