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29 May 2023, 00:17
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
67% (02:44) correct
33%
(02:40)
wrong
based on 217
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A police car was chasing a thief riding a motorcycle. The thief had a head start of 60 mins and was traveling at a speed of 40 miles per hour. However, 30 mins after the police car had started chasing the motorcycle, the thief stopped his motorcycle for 15 mins at a gas station and then continued the run. If the police car was traveling at a speed of 60 miles per hour, after how much time since the police started, will they catch the thief?
A. 1 hour
B. 1.5 hours
C. 2 hours
D. 2.25 hours
E. 2.5 hours
A. 1 hour
B. 1.5 hours
C. 2 hours
D. 2.25 hours
E. 2.5 hours
29 May 2023, 02:35
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ChandlerBong
As the thief had a head start of 60 mins, the thief had traveled 40 miles when the police started the chase.
At the end of the 90th minute (i.e. 30 mins after the police started the chase), the thief had covered a distance of 40 + 20 = 60 miles and the police had covered a distance of 30 miles.
The thief took a break between the 90th and 105th minute, so the distance traveled by the thief is zero, while the police covered a distance of 15 miles. So at the end of the 105th minute, the police had covered 45 miles while the thief had covered 60 miles.
The chase continues, and the 15-mile gap was covered in \(\frac{15}{60-40}\) hours.
Time taken to cover the gap distance = \(\frac{15}{60-40} = \frac{3}{4}\) hour = 45 mins.
Time elapsed since the police started the chase = 30 minutes + 15 mins + 45 mins = 1.5 hours
Option B
General Discussion
29 May 2023, 03:15
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ChandlerBong
The thief had a head start of 60 minutes.
The thief was traveling at a speed of 40 miles per hour.
The police car was traveling at a speed of 60 miles per hour.
The thief stopped at a gas station for 15 minutes.
The police car started chasing the thief 30 minutes after the thief had left the gas station.
The thief had traveled for 60 + 30 = 90 minutes before the police car started chasing him.
In those 90 minutes, the thief had traveled 90 * 40/60 = 60 miles.
In the 30 minutes that the police car was chasing him, the police car had traveled 30 * 60/60 = 30 miles.
So, the thief is 60 - 30 = 30 miles ahead of the police car.
The police car is traveling at a speed of 60 miles per hour, and the thief is traveling at a speed of 40 miles per hour.
The police car can catch the thief in 30 / (60 - 40) = 1.5 hours.
So the answer is (B).
