Two cars start out simultaneously from a point in the same direction, one of them going at a speed 50kmph and the other at 40kmph. In half an hour a third car starts out from the same point and overtakes the first car 1.5 hours after catching up with the second car. Find the speed of the third car.
Answers
velocity of 3rd car is 60 Km/hr
•After 1/2 hour
•second car will be at 20 km from starting point
•first car will be at 25 km from starting point
•Let the spped of third car is V km/hr
& it takes time t to catch second car
•So, Distance covered by 3rd car in t = 20 + Distance covered by 2nd car in t
V×t = 20 + 40t
t = 20/(V-40) _____(1)
•Now in time t distance between 2nd car and 1st car will become
5 + (50-40)×20/(V-40)
= (5v)/(v-40) ________(2)
•Now,
Third car takes 3/2 hours to overtake first car
distance by 3rd car = (5v)/(v-40) +
50(3/2)
3v = (10v + 150v - 6000)(v-40)
3v²-120v = 160v - 6000
3v²-280v + 6000 = 0
3v²-180v - 100v + 6000 = 0
3v(v-60) -100(v -60) = 0
(v-60)(3v-100) = 0
v = 60 & v = 100/3
• v = 100/3 is not possible because to overtake spped must be greater than 1st &2nd car
•so, velocity of 3rd car is 60 Km/hr
Pls refer the attachment
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