Select the correct answerA thief is spotted by a policeman from a distance of 100 m. When the policeman starts the chase, the thief also starts running. If the speed of the thief is 8 km/hour and police is 10 km/ hour, then how far will the thief have to run before he is overtaken?Options200 m400 m500 m300 m
Question
Select the correct answerA thief is spotted by a policeman from a distance of 100 m. When the policeman starts the chase, the thief also starts running. If the speed of the thief is 8 km/hour and police is 10 km/ hour, then how far will the thief have to run before he is overtaken?Options200 m400 m500 m300 m
Solution
To solve this problem, we need to understand that the policeman and the thief are moving in the same direction. The effective speed of the policeman relative to the thief is the difference of their speeds.
Step 1: Convert the speeds from km/hour to m/sec because the distance is given in meters. 1 km/hour = 1000 m/3600 sec = 5/18 m/sec.
So, the speed of the thief = 8 km/hour = 8 * 5/18 = 20/9 m/sec. And, the speed of the policeman = 10 km/hour = 10 * 5/18 = 50/9 m/sec.
Step 2: Calculate the relative speed of the policeman with respect to the thief. Relative speed = Speed of policeman - Speed of thief = 50/9 - 20/9 = 30/9 = 10/3 m/sec.
Step 3: Calculate the time it takes for the policeman to catch the thief. The initial distance between them is 100 m. The time it takes to cover this distance with the relative speed is Time = Distance/Speed = 100/(10/3) = 30 seconds.
Step 4: Calculate the distance the thief runs in this time. Distance = Speed * Time = (20/9) * 30 = 200 m.
So, the thief will have to run 200 m before he is overtaken. The correct answer is 200 m.
Similar Questions
Select the correct answerA thief runs at a speed of 10 m/s. A Policeman runs behind him at a speed of 12.5 m/sec but after 10 seconds the Policeman had started running. After how many meters, will the Policeman catch the thief?Options600 mtr400 mtr300 mtr500 mtr
A policeman follows a thief, who is 1250 m ahead of him. The policeman and the thief run at the speed of 10 km/h and 8 km/h, respectively. The distance (in km) run by the thief before he is nabbed by the policeman is
A thief is noticed by a policeman from a distance of 750m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 13 km per hour and 10 km per hour respectively. What is the distance between them after 10 minutes?a.410 meterb.300 meterc.400 meterd.250 meter
YouA police chases a thief. Their respective speeds are 8 and 6 km/hr. If the police started 10 min late, at what distance he will catch the thief
Select the correct answerA thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes ?radio_button_unchecked100 mradio_button_unchecked150 mradio_button_unchecked190 mradio_button_unchecked200 m
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.