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Bunuel
A thief steals a car at 2.30 p.m. and drives it at 60 km/h. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/h. When will he overtake the thief?

(A) 4.30 p.m.
(B) 4.45 p.m.
(C) 5 p.m.
(D) 5.15 p.m.
(E) 5.20 p.m.
Solution:

We can let t be the time, in hours, that it will take the owner of the car to overtake the thief. We can create the equation:

60(t + 1/2) = 75t

60t + 30 = 75t

30 = 15t

2 = t

Therefore, it takes 2 hours for the owner of the car to overtake the thief. Since he starts at 3 pm, he overtakes the thief at 5 pm.

Answer: C
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Bunuel
A thief steals a car at 2.30 p.m. and drives it at 60 km/h. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/h. When will he overtake the thief?

(A) 4.30 p.m.
(B) 4.45 p.m.
(C) 5 p.m.
(D) 5.15 p.m.
(E) 5.20 p.m.

This is a catch up problem, where the time being asked is when the owner will overtake the thief. They will have both traveled the same distance when the owner overtakes the thief.

We know that the thief has traveled an additional 30 mins because they left at 2:30 p.m.

Thief Distance = 60 km/h * (t + 0.5)

Owner Distance = 75 km/h * t

We can set these two equations equal to each other to find t.

60t + 30 = 75t
30 = 15t
2 = t

It would take the owner 2 hours to overtake the thief. Since the owner left at 3 pm, he will overtake the thief at 3 pm + t =

3 pm + 2 hours = 5 p.m.

Option C

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