How Many Cars?(INPHO 2007)

Classical Mechanics Level 3

A car leaves point A for point B every ten minutes. The distance between A and B is 60 Km. The car travels at a speed of 60 km/hr.

What is the number of cars that a man driving from B to A will meet in route, if he starts from B simultaneously from one of the cars leaving A. The car from B also travels at 60 km/hr.

A question is a bit ambiguous and hence there can be two possible answers say (16,18). You have to figure out which are the two possible answers

HINT:-
1) Understand the question properly
2) Do it Graphically.

Image credit: Wikipedia Jonathan Wiklins

(5,6) (12,13) (11,13) (6,8)

2 solutions

Emanuel Sygal
Aug 7, 2014

When our car starts from B there are 7 cars on the route that started from A, and we will meet all of them. For every 10km a new can starts from A and will meet us too. so there are 6 more, a total of 13. And one could argue that we don't really meet a car when we arrive or start our journey, so 11.

But the official answer given is 13.

Tushar Gopalka - 6 years, 10 months ago

Cars are 10 km. apart. Relative speed of crossing is 60 - (- 60)=120km/hr=2km/minuets. So each car is at 10/2=5 minuets away.
For 60 minuets journey, he meets 60/5 =12 cars including at A + he
met one at B, =13cars, 11 in the road. Just another method.

Niranjan Khanderia - 6 years, 5 months ago

Shuvam Keshari
Sep 14, 2015

the dark lines represent the 2 stations.

the cars leaving A have been plotted with respect to their position time graph. (there will be a number of them) but only the required ones have been shown. now take another car from B towards A shown by the line ap. the number of intersections give the result!!

if we do not consider the end points (which we should, bcoz, "en route" means "on the way") then we get the answer=11

otherwise it is 13!!

How Many Cars?(INPHO 2007)

Image credit: Wikipedia Jonathan Wiklins

2 solutions

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