Question
Download Solution PDFA person cycles from hostel to college at a speed of 20 kmph and reaches 13.5 minutes late. If he cycles at a speed of 24 kmph and reaches early by 13.5 minutes, find the distance between hostel and college. (in km)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Speed at which the person is late = 20 kmph
Time late = 13.5 minutes = 13.5/60 = 0.225 hours
Speed at which the person is early = 24 kmph
Time early = 13.5 minutes = 13.5/60 = 0.225 hours
Formula Used:
Distance (D) = Speed × Time
Time difference = Difference in distances / Relative speed
Calculation:
Let the distance between the hostel and college = D km.
Time taken at 20 kmph = D / 20
Time taken at 24 kmph = D / 24
Time difference = (D / 20) - (D / 24)
It is given that the total time difference is the sum of 13.5 minutes late and 13.5 minutes early, which is 27 minutes = 27 / 60 = 0.45 hours.
⇒ (D / 20) - (D / 24) = 0.45
Taking LCM of 20 and 24:
⇒ (6D - 5D) / 120 = 0.45
⇒ D / 120 = 0.45
⇒ D = 0.45 × 120
⇒ D = 54 km
The distance between the hostel and college is 54 km.
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