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ఒక వ్యక్తి 2.5 గంటల పాటు గంటకు 53 కి.మీ. వేగంతో ప్రయాణించాడు, ఆపై తన వేగాన్ని గంటకు 28 కి.మీ. మేర పెంచి, మరో గంటలో గమ్యాన్ని చేరుకున్నాడు. ఆ వ్యక్తి తన మొత్తం ప్రయాణంలో సాధించిన సగటు వేగాన్ని (గంటకు కి.మీ.లలో) కనుగొనండి?
59
58
60
61
61
Calculate distance: (53 × 2.5) + (81 × 1) = 132.5 + 81 = 213.5. Total time = 3.5. Average = 213.5 / 3.5 = 61.
Speed 1 = 53 kmph for Time 1 = 2.5 hours. Speed 2 = 53 + 28 = 81 kmph for Time 2 = 1 hour.
Average Speed=Total TimeTotal Distance=t1+t2d1+d2
Calculate distance: (53 × 2.5) + (81 × 1) = 132.5 + 81 = 213.5. Total time = 3.5. Average = 213.5 / 3.5 = 61.
Many students mistake 'increased his speed by 28' as the new speed (28 kmph) instead of adding it to the original speed (53 + 28 = 81 kmph).
Calculate distance for the first part
Distance d1=Speed×Time=53×2.5.
d1=132.5 km
Calculate speed and distance for the second part
The speed increased by 28 kmph, so new speed is 53+28=81 kmph for 1 hour.
d2=81×1=81 km
Calculate Total Distance and Total Time
Total distance = 132.5+81=213.5 km. Total time = 2.5+1=3.5 hours.
Dtotal=213.5 km,Ttotal=3.5 hours
Final calculation of Average Speed
Divide total distance by total time: 213.5/3.5.
Avg Speed=3.5213.5=61 kmph
D is correct because the average speed calculated using total distance (213.5 km) divided by total time (3.5 hours) is 61 kmph.
This concept is foundational for 'Relative Speed' and 'Trains' problems, where calculating total distance covered at varied speeds is the primary step.