Question #23929

A thief steals a car at 1.30p.m. and drives it at 45km an hour. The theft is discovered at 2p.m. and the owner sets off in another car at 50km an hour .He will overtke the thief at?

Expert's answer

Lett is a time in hours after 2p.m that owner spend to overtake the thief.

Then the distance that thief drives by time t is 45*(0.5 + t) km and the

distance that drives owner is 50*t km. So we have the equation:

45*(0.5 + t) = 50*t

27.5 + 45t = 50t

(50 - 45)t = 27.5

5t = 27.5

t = 5.5 hours

So, owner will overtake the thief at 7.30p.m.

Then the distance that thief drives by time t is 45*(0.5 + t) km and the

distance that drives owner is 50*t km. So we have the equation:

45*(0.5 + t) = 50*t

27.5 + 45t = 50t

(50 - 45)t = 27.5

5t = 27.5

t = 5.5 hours

So, owner will overtake the thief at 7.30p.m.

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