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Two cyclists A and B start from the same place at the same time, one going towards north at 18 km/hr and other going towards south at 20 km/hr. What time will they take to be 95 km apart?
- a)4 hrs 30 min
- b)4 hrs 45 min
- c)5 hrs 16 min
- d)2 hrs 30 min
Correct answer is option 'D'. Can you explain this answer?
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Solution:
Let's assume that the time taken by the cyclists to be 95 km apart is 't' hours.
Distance Travelled by Cyclist A:
The distance travelled by Cyclist A in 't' hours is given by:
Distance = Speed × Time
Distance = 18 km/hr × t hours
Distance = 18t km
Distance Travelled by Cyclist B:
The distance travelled by Cyclist B in 't' hours is given by:
Distance = Speed × Time
Distance = 20 km/hr × t hours
Distance = 20t km
Relative Distance:
The relative distance between the cyclists is the sum of the distances travelled by each of them in opposite directions. Therefore,
Relative Distance = Distance Travelled by Cyclist A + Distance Travelled by Cyclist B
Relative Distance = 18t + 20t
Relative Distance = 38t km
Given Condition:
It is given that the cyclists are 95 km apart. Therefore,
38t = 95
t = 95/38
t = 2.5 hours
Conversion to Minutes:
To convert the time from hours to minutes, we multiply by 60.
t = 2.5 × 60
t = 150 minutes
Conversion to Hours and Minutes:
Since the question asks for the time in hours and minutes, we divide the total minutes by 60 to get the hours and take the remainder as the minutes.
t = 150 minutes = 2 hours 30 minutes
Therefore, the cyclists will take 2 hours 30 minutes to be 95 km apart.
Let's assume that the time taken by the cyclists to be 95 km apart is 't' hours.
Distance Travelled by Cyclist A:
The distance travelled by Cyclist A in 't' hours is given by:
Distance = Speed × Time
Distance = 18 km/hr × t hours
Distance = 18t km
Distance Travelled by Cyclist B:
The distance travelled by Cyclist B in 't' hours is given by:
Distance = Speed × Time
Distance = 20 km/hr × t hours
Distance = 20t km
Relative Distance:
The relative distance between the cyclists is the sum of the distances travelled by each of them in opposite directions. Therefore,
Relative Distance = Distance Travelled by Cyclist A + Distance Travelled by Cyclist B
Relative Distance = 18t + 20t
Relative Distance = 38t km
Given Condition:
It is given that the cyclists are 95 km apart. Therefore,
38t = 95
t = 95/38
t = 2.5 hours
Conversion to Minutes:
To convert the time from hours to minutes, we multiply by 60.
t = 2.5 × 60
t = 150 minutes
Conversion to Hours and Minutes:
Since the question asks for the time in hours and minutes, we divide the total minutes by 60 to get the hours and take the remainder as the minutes.
t = 150 minutes = 2 hours 30 minutes
Therefore, the cyclists will take 2 hours 30 minutes to be 95 km apart.
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