एका passenger गाडीला वर्धा ते अकोला हे 240 किलोमीटर अंतर जाण्यासाठी जलद गाडीपेक्षा 2 तास अधिक लागतात . जर passenger गाडीचा वेग जलद गाडीपेक्षा 20 किलो/तास ने कमी असेल तर दोन्ही गाड्यांचा सरासरी वेग किती असेल?
Answers
Given : passenger गाडीला वर्धा ते अकोला हे 240 किलोमीटर अंतर जाण्यासाठी जलद गाडीपेक्षा 2 तास अधिक लागतात . जर passenger गाडीचा वेग जलद गाडीपेक्षा 20 किलो/तास
Passenger train takes 2 hr more than faster train to cover distance of 240 km
Passenger train speed is 20 km/hr less than faster train
To Find : दोन्ही गाड्यांचा सरासरी वेग
Speed of both trains
Solution:
Distance = 240 km
Speed of Faster Train = S km/hr
Speed of Passenger Train = S - 20 km/hr
Time = Distance/ Speed
Time taken by Faster Train = 240/S hrs
Time taken by Passenger Train = 240/(S- 20) hrs
240/(S- 20) = 240/S + 2
=> 240S = 240(S - 20) + 2(S)(S - 20)
=> 120S = 120(S - 20) + (S)(S - 20)
=> 120S = 120S - 2400 + S² - 20S
=> S² - 20S - 2400 = 0
=> S² - 60S + 40S - 2400 = 0
=> (S - 60)(S + 40) = 0
=> S = 60
Speed of Faster Train = 60 km/hr
Speed of Passenger Train = 40 km/hr
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