Question
- A thief steals a motor car at 1 p.m. and drives it at 45 km/hr. The theft is discovered at 2 p.m. and the owner sets off in another car at 54 km/hr. When will he overtake the thief?
Answer: Option A
The question states that a thief has stolen a motor car at 1 pm and is driving it at 45 km/hr. The theft is discovered at 2 pm and the owner sets off in another car at 54 km/hr to catch the thief. To calculate when the owner will catch up to the thief, we must first calculate the total distance between them.
We can use the following formula to calculate the total distance between the thief and the owner:
Total Distance = (Thief's Speed × Time) - (Owner's Speed × Time)
In this case, the total distance is:
Total Distance = (45 km/hr × 1 hr) - (54 km/hr × 1 hr)
Total Distance = 45 km - 54 km
Total Distance = -9 km
This means that the thief is 9 km ahead of the owner at the beginning of the chase.
Now, we can use the following formula to calculate the time it will take for the owner to catch up to the thief:
Time = (Total Distance)/(Owner's Speed - Thief's Speed)
In this case, the time is:
Time = (-9 km)/(54 km/hr - 45 km/hr)
Time = (-9 km)/(9 km/hr)
Time = 1 hour
Therefore, it will take the owner 1 hour to catch up to the thief. Since the owner started chasing at 2 pm, he will catch up to the thief at 7 pm.
Hence, the correct answer is Option A - 7 p.m.
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The question states that a thief has stolen a motor car at 1 pm and is driving it at 45 km/hr. The theft is discovered at 2 pm and the owner sets off in another car at 54 km/hr to catch the thief. To calculate when the owner will catch up to the thief, we must first calculate the total distance between them.
We can use the following formula to calculate the total distance between the thief and the owner:
Total Distance = (Thief's Speed × Time) - (Owner's Speed × Time)
In this case, the total distance is:
Total Distance = (45 km/hr × 1 hr) - (54 km/hr × 1 hr)
Total Distance = 45 km - 54 km
Total Distance = -9 km
This means that the thief is 9 km ahead of the owner at the beginning of the chase.
Now, we can use the following formula to calculate the time it will take for the owner to catch up to the thief:
Time = (Total Distance)/(Owner's Speed - Thief's Speed)
In this case, the time is:
Time = (-9 km)/(54 km/hr - 45 km/hr)
Time = (-9 km)/(9 km/hr)
Time = 1 hour
Therefore, it will take the owner 1 hour to catch up to the thief. Since the owner started chasing at 2 pm, he will catch up to the thief at 7 pm.
Hence, the correct answer is Option A - 7 p.m.
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Therefore time needed = 1hr(2-1)
Distance when theft has discovered =
45*1= 45km
Time when the theft has discovered =
(45km) /9(54-45)km/hr = 5hr
Time = 2pm + 5hr = 7pm