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Speed time distance

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Speed Time Distance CAT basics

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Speed time distance

  1. 1. 2IIM Ascent Education’s An IIM Alumni Venture Speed Time Teaching Notes – 2IIM
  2. 2. 2IIM Ascent Education’s An IIM Alumni Venture Theory Speed Time Distance - Basic concepts 2 Speed = Kindly make sure that the units used are consistent. 1 km = 1000m 1 mile = 1.6 kms = 1600 mts 1 hr = 60 minutes = 3600 seconds 1 km/hr = 1000m/hour = 1000m/3600 seconds or 5/18 m/s 1m/s = (1/1000) km/ (1/3600) hours = 18/5 km/hr To convert km/hr to m/s, multiply by 5/18 To convert from m/s to km/hr, multiply by 18/5 Time Distance
  3. 3. 2IIM Ascent Education’s An IIM Alumni Venture Question 3 Travelling at of his usual speed, Arvind reaches the restaurant 10 minutes early. How long did he take to reach the restaurant this time? Q. th 8 9
  4. 4. 2IIM Ascent Education’s An IIM Alumni Venture Solution 4 Travelling at of his usual speed, Arvind reaches the restaurant 10 minutes early. How long did he take to reach the restaurant this time? of usual speed implies that it takes of usual time for Arvind to reach the restaurant. He saves of usual time. This corresponds to 10 mins. Thus, the usual timing = 9 * 10 = 90 mins Since he reached 10 mins earlier 90 - 10 = 80 mins is the time taken by Arvind to reach the restaurant today. A. th 8 9 th 9 8 th 8 9 th 9 1
  5. 5. 2IIM Ascent Education’s An IIM Alumni Venture Question 5 Cycling at a speed of 10 km/h from his residence, Rajesh reached the railway station 3 minutes late. Had he cycled at a speed of 12 km/h he would have reached 3 minutes early. What is the distance between his house and the railway station? Q.
  6. 6. 2IIM Ascent Education’s An IIM Alumni Venture Solution 6 Cycling at a speed of 10 km/h from his residence, Rajesh reached the railway station 3 minutes late. Had he cycled at a speed of 12 km/h he would have reached 3 minutes early. What is the distance between his house and the railway station? Distance covered in both cases is the same Speed Time 10 kmph t + hrs 12 kmph t - hrs A. 60 3 60 3
  7. 7. 2IIM Ascent Education’s An IIM Alumni Venture Solution 7 So we equate them. 10 * (t + ) = 12 * ( t - ) 2t = t = Distance = 12 * = 6 km Therefore, The distance between his house and the railway station is 6 km. 60 3 60 3 10 11 10 56 2 1 5 3 = + =+ 20 11 60 360 60 3 20 11 =      −
  8. 8. 2IIM Ascent Education’s An IIM Alumni Venture Theory Speed Time Distance – Some prototypes 8  A travels from point X to Y a distance of 100 km, B who starts at the same time as A starts from point Y and moves towards X. If A and B travel at a km/hr and b km/hr respectively, after how long will they meet?  When they meet, both should have travelled the same amount of time. Or =  Travelling at 8/7 th of his usual speed, Arvind reaches the restaurant 10 minutes early. How long did he take to reach the restaurant this time  The distance travelled in both cases is the same. So, if Arvind travels at of his usual speed, he will take of his usual time a x b x-100 th 7 8 th 8 7
  9. 9. 2IIM Ascent Education’s An IIM Alumni Venture Theory Speed Time Distance – Average speed and relative speed 9  Average Speed =  Relative speed is the speed at which one object is approaching or receding from another.  When A and B travel in the same direction, relative speed = Sa - Sb  When A and B travel in opposite directions, relative speed = Sa + Sb  All the formulae that we use in the normal context can be extended to relative speeds also.  Relative speed =  Relative Distance = Relative Speed * Time TimeTotal DistanceTotal Time DistanceRelative
  10. 10. 2IIM Ascent Education’s An IIM Alumni Venture Question 10 Anand travels the first 30 minutes of the journey at a speed of 80 kmph and the balance 90 minutes of his journey at a speed of 40 kmph. What is the average speed of his journey in kmph? Q.
  11. 11. 2IIM Ascent Education’s An IIM Alumni Venture Solution 11 Anand travels the first 30 minutes of the journey at a speed of 80 kmph and the balance 90 minutes of his journey at a speed of 40 kmph. What is the average speed of his journey in kmph? Distance travelled during the first 30 minutes = 80 * = 40 km. ( since the speed is in kmph we are converting the 30 minutes to hour) Distance covered during the next 90 minutes = 40 * = 60 km. Total Distance travelled = 40 + 60 = 100 km Time taken = 2 hours Average speed = 100/2 = 50 km/hr A. 60 30 60 90
  12. 12. 2IIM Ascent Education’s An IIM Alumni Venture Question 12 A car covers a third of the distance between two cities at a speed of 30 kmph and the balance distance at a speed of 60 kmph. What is the average speed of the car? Q.
  13. 13. 2IIM Ascent Education’s An IIM Alumni Venture Solution 13 A car covers a third of the distance between two cities at a speed of 30 kmph and the balance distance at a speed of 60 kmph. What is the average speed of the car? Let us assume the overall distance = 90 km. The car travels the first 30km at 30 kmph and the remaining 60 km at 60 kmph. Total time taken = 30/30 + 60/60 = 2 hours. Average speed = 90/2 = 45kmph A.
  14. 14. 2IIM Ascent Education’s An IIM Alumni Venture Question 14 Ram leaves Bangalore at 4 PM in his car and travels to Chennai at 50 kmph. Shyam leaves Chennai at 5 PM and travels in his bike at 60 kmph to Bangalore along the same route. If the distance between Bangalore and Chennai is 380 kms, when will Ram and Shyam meet and how far from Bangalore will they meet? Q.
  15. 15. 2IIM Ascent Education’s An IIM Alumni Venture Solution 15 Ram leaves Bangalore at 4 PM in his car and travels to Chennai at 50 kmph. Shyam leaves Chennai at 5 PM and travels in his bike at 60 kmph to Bangalore along the same route. If the distance between Bangalore and Chennai is 380 kms, when will Ram and Shyam meet and how far from Bangalore will they meet? The relative speed between them = 50 + 60 = 110 kmph When Shyam started, distance travelled by Ram = 1 * 50 = 50 km. The distance between the two at 5 PM = 380 - 50 = 300 km. Time at which they meet = = 3 hours 3 hours from 5 PM is 8 PM A. 110 330
  16. 16. 2IIM Ascent Education’s An IIM Alumni Venture Solution 16 So in total Shyam travels 3 hours when they meet. Distance travelled by Shyam in 3 hours = 3 * 60 = 180 km. So they meet at a point 200km from Bangalore.
  17. 17. 2IIM Ascent Education’s An IIM Alumni Venture Question 17 A train travelling at a speed of 72 mph crosses a platform of length 1400 meters completely in 60 seconds. What is the length of the train in meters. Use conversion: 1 mile = 1600 meters Q.
  18. 18. 2IIM Ascent Education’s An IIM Alumni Venture Solution 18 A train travelling at a speed of 72 mph crosses a platform of length 1400 meters completely in 60 seconds. What is the length of the train in meters. Use conversion: 1 mile = 1600 meters Distance travelled by the train = length of the train + length of the platform. Distance covered by train in 60 sec = 72* * 1.6 * 60 ( is the conversion of speed from mph to meters per second) = 1920 m. Length of the train = 1920 - length of the platform = 1920 - 1400 = 520 m A. 18 5 18 5
  19. 19. 2IIM Ascent Education’s An IIM Alumni Venture Question 19 A passenger train traveling at 70 kmph crosses a freight train, of length 400 m traveling in the opposite direction at a speed of 38 kmph, completely in 25 seconds. What is the length of the passenger train in meters? Q.
  20. 20. 2IIM Ascent Education’s An IIM Alumni Venture Solution 20 A passenger train traveling at 70 kmph crosses a freight train, of length 400 m traveling in the opposite direction at a speed of 38 kmph, completely in 25 seconds. What is the length of the passenger train in meters? Relative speed = 70 + 38 = 108 kmph Distance covered = 25 * 108 * = 750 meters But, Distance covered = length of train A + length of train B 750 = 400 + length of passenger train Therefore length of passenger train = 750 - 400 = 350 m A. 18 5
  21. 21. 2IIM Ascent Education’s An IIM Alumni Venture Question 21 A boat travels from city A to city B, a distance of 72 km. The onward journey is a downstream journey and the return journey is an upstream one. If the round trip took the boat 7 hours and the speed of the stream is 3 kmph, what was its speed in the return journey? Q.
  22. 22. 2IIM Ascent Education’s An IIM Alumni Venture Solution 22 A boat travels from city A to city B, a distance of 72 km. The onward journey is a downstream journey and the return journey is an upstream one. If the round trip took the boat 7 hours and the speed of the stream is 3 kmph, what was its speed in the return journey? Let ‘x’ be the speed of the boat in Still water. Now , the total distance covered = 144 km Upstream speed = x - 3 Downstream speed = x + 3 Time taken to travel 72 km upstream = Time taken to travel 72 km downstream = Total time = 7 hours A. 3x 72 − 3x 72 +
  23. 23. 2IIM Ascent Education’s An IIM Alumni Venture Solution 23 = 7 = 7 72x - 216 + 72x + 216 = 7x2 - 63 7x2 - 144x - 63 = 0 The solutions are x = 21 or x = - 3, speed can’t be negative. Thus, x = 21 And the upstream speed = x - 3 = 21 - 3 = 18 kmph Speed of the boat during the return journey = 18 kmph 3x 72 3x 72 − + + 9x 3)72(x3)72(x 2 − ++−

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