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# Races

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### Races

1. 1. 2IIM Ascent Education’s An IIM Alumni Venture Races • Teaching Notes – Ascent Education
2. 2. 2IIM Ascent Education’s An IIM Alumni Venture Question In a 100m race, A can give B a start of 12 meters or 3 seconds. What is the speed of B in m/sec and how long will A take to run 100m? 1.
3. 3. 2IIM Ascent Education’s An IIM Alumni Venture Solution 3 In a 100m race, A can give B a start of 12 meters or 3 seconds. What is the speed of B in m/sec and how long will A take to run 100m? A can give B a start of 12 meters or 3 second start => B covers 12 meters in 3 sec So, speed of B = = 4 meters/sec Time taken for B to complete the race = = 25 sec Since A gives B a start of 3 sec, A completes the race 3 seconds before B. Thus time taken by A to run 100 meters = 25 - 3 = 22 sec 1. 3 12 4 100
4. 4. 2IIM Ascent Education’s An IIM Alumni Venture Question A can give B a start of 30 in a km race and A can give C a start of 50m in a km race. How much start will B be able to give C in a km race? 2.
5. 5. 2IIM Ascent Education’s An IIM Alumni Venture Solution A can give B a start of 30m in a km race and A can give C a start of 50m in a km race. How much start will B be able to give C in a km race? A can give B start of 30 m or, when B travels 970 m, A can cover 1000 m. A B C 1000 970 950 1000 ? = X 2. B A 970 m 1000 m
6. 6. 2IIM Ascent Education’s An IIM Alumni Venture Solution When A covers 1000 m, B covers 970, C covers 950. The Qn is when B covers 1000 m, how much would C cover X = = Or the lead B should give B = 1000 - X = m = 20.61 m 970 950*1000 97 95000 97 95000 97 2000
7. 7. 2IIM Ascent Education’s An IIM Alumni Venture Question A runs a 400m race at the speed of 8 m/sec. He gives B a start of 40m and still beats him by 10 seconds. What is B's speed? 3.
8. 8. 2IIM Ascent Education’s An IIM Alumni Venture Solution A runs a 400m race at the speed of 8 m/sec. He gives B a start of 40m and still beats him by 10 seconds. What is B's speed? A takes 50 seconds. B travels 360 m in 60 seconds. Or, B travels @ 6 m/s. 3.
9. 9. 2IIM Ascent Education’s An IIM Alumni Venture Question If A gives B a start of 20m in a race, A beats him by 10 seconds. On the contrary, if A gives B a start of 40m, they finish the race in a dead heat. If the length of the race is 400m, how long will A take to run the race? 4.
10. 10. 2IIM Ascent Education’s An IIM Alumni Venture Solution If A gives B a start of 20m in a race, A beats him by 10 seconds. On the contrary, if A gives B a start of 40m, they finish the race in a dead heat. If the length of the race is 400m, how long will A take to run the race? A’s speed = A B’s Speed = B 10B = 9A 4. B 360 A 400 = 10 B 380 A 400 −= 10 B 360 B 380 =− 10 B 20 =
11. 11. 2IIM Ascent Education’s An IIM Alumni Venture Solution B = 2 m/s B takes 180 seconds to run 360m. A will take 180 seconds to run the race.
12. 12. 2IIM Ascent Education’s An IIM Alumni Venture Question A and B start around a circular track of length 600m at speeds of 6m/s and 9 m/sec from the same point, simultaneously and in the same direction. When will they meet for the first time? How far from the starting point will they meet, when they meet for the first time? 5.
13. 13. 2IIM Ascent Education’s An IIM Alumni Venture Solution A and B start around a circular track of length 600m at speeds of 6m/s and 9 m/sec from the same point, simultaneously and in the same direction. When will they meet for the first time? How far from the starting point will they meet, when they meet for the first time? Track length = 600 m A’s speed = 6 m/s B’s speed = 9 m/s Rd speed = 3 m/s Meet for the first time after - = 200 seconds. In 200 s, A travels 200 x 6 = 1200 m. So they meet @ the starting point. 5. 3 600
14. 14. 2IIM Ascent Education’s An IIM Alumni Venture Question A and B run around a circular track at speeds of 8m/sec and 5m/sec starting from the same point, simultaneously and in the same direction. How many points with respect to the starting point on the circular track will they meet, if the run at the above mentioned constant speeds endlessly? 6.
15. 15. 2IIM Ascent Education’s An IIM Alumni Venture Solution A and B run around a circular track at speeds of 8m/sec and 5m/sec starting from the same point, simultaneously and in the same direction. How many points with respect to the starting point on the circular track will they meet, if the run at the above mentioned constant speeds endlessly? Track length = T A’s speed = 8 m/s B’s speed = 5 m/s Relative speed = 8 - 5 = 3 m/s They meet after seconds. Time taken for A to finish a lap = 6. 2 T a T
16. 16. 2IIM Ascent Education’s An IIM Alumni Venture Solution Time taken for B to finish a lap = Time after which they meet at the starting point = LCM = No of positions = Time to meet @ = = 2. b T       b T a T , 1 T b)(a,HCF T =            meet1forTime pointStarting st T/2 T/1 No of positions =       b)(a,HCF b-a