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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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એક વ્યક્તિ 2.5 કલાક માટે 53 કિમી પ્રતિ કલાકની ઝડપે વાહન ચલાવે છે, પછી તેની ઝડપ 28 કિમી પ્રતિ કલાક વધારી અને બીજા એક કલાકમાં ગંતવ્ય સ્થાને પહોંચી જાય છે. તે વ્યક્તિની સમગ્ર યાત્રા દરમિયાનની સરેરાશ ઝડપ (કિમી પ્રતિ કલાકમાં) શોધો.
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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.