: Speed up with math equations #IndiaNEWS #Education Today Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some

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Speed up with math equations #IndiaNEWS #Education Today
Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and solutions on the Average Speed topic.
The general average and average speed are not same. Here, we should use different formulas:
1. If a person travelled two equal distances at x km/hr and y km/hr, then
Average Speed = 2xy/x y km/hr
2. If a person travelled three equal distances at x km/hr, y km/hr and z km/hr, then
Average Speed = 3xyz/xy yz zx km/hr
3. If a person travelled two or more than two, equal or unequal distances at different speeds, then
Average Speed = Total Distance / Total Time
4. A person travels first half of the total time with speed x km/hr and second half time with speed y km/hr, then
Average Speed = x y / 2
Practice questions
1. A person travelled from his house to office at 60 km/hr and office to house at 90 km/hr. Then find his average speed?
Solution:
Here, the average of 60 and 90 is not right answer.
The average speed = 2xy/x y km/hr = 2 × 60 × 90 / 150 = 72 km/hr
2. A speeding car travelling at 40 km/hr decides to slow down to 30 km/hr after covering half the distance. What is the average speed?
Solution:
Here, the first half of the distance and remaining distance, both are same
Then average speed = 2xy/ x y km/hr = 2 × 40 × 30 / 70 = 34. 29 km/hrs
3. A person travelled first 5 hours at 40 km/hr and next 5 hours at 50 km/hr. Then find his average speed?
Solution:
If a person travelled two equal times at different speeds, the average speed is equal to average of two speeds
Average speed = 40 60 / 2 = 100 / 2 = 50 km/hr
4. A person travelled three equal distances at 20 km/hr, 30 km/hr and 60 km/hr. Then find his average speed?
Solution:
Average speed = 3xyz / xy yz zx
= 3 × 20 × 30 × 60 / 20×30 30×60 60×20
= 3 × 20 × 30 × 60 / 3600 = 30 km/hr
5. Shekar drove for 3 hours at a rate of 50 km/hr and for 2 hours at 60 km/hr. What was his average speed for the whole journey?
Solution:
Total distance = 3 × 50 2 × 60 = 150 120 = 270 km/hr
Total time = 3 2 = 5 hours
Average speed = Total Distance / Total Time = 270 / 5 = 54 km/hr
6. On Rekha drive to her aunt’s house, the traffic was light, and she drove the 45 km in one hour. However, the return trip took her two hours. What was her average speed for the round trip?
Solution:
Average speed = Total Distance / Total Time = 45 45/1 2 90/3 = 30 km/hr
7. A person completes a journey in 12 hours. He travels first half of the journey at the rate of 30 km/hr and second half at the rate of 50 km/hr. Find the total journey in km.
Solution:
Average speed = 2 × 3 × 50/ 30 50 = 2 × 30 × 50 / 80 75/2 km/hr
Time = 12 hours
Total distance = 12 × 75/2 = 450 km
8.

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