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Updated on: 24 Feb 2024, 10:55
Originally posted by EgmatQuantExpert on 09 May 2018, 08:31.
Last edited by Bunuel on 24 Feb 2024, 10:55, edited 6 times in total.
Last edited by Bunuel on 24 Feb 2024, 10:55, edited 6 times in total.
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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69% (02:20) correct
31%
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wrong
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A straight highway connects two cities P and Q, and goes via two checkpoints M and N, in that order. A bus started from P and moved to M at an average speed of 30 mph. After crossing M, it increased its speed to 50 mph and moved towards N. When it reached N, it further increased its speed to 60 mph and continued to move at this speed till it reached Q. What is the average speed of the bus throughout the whole journey?
(1) The ratio of time the bus took to cover the distances PM, MN, and NQ respectively is 2:1:3
(2) Out of the three distances, NQ is 3 times the distance PM and more than 3 times the distance MN
(1) The ratio of time the bus took to cover the distances PM, MN, and NQ respectively is 2:1:3
(2) Out of the three distances, NQ is 3 times the distance PM and more than 3 times the distance MN
Application of Average Speed in Distance problems - Exercise Question #1
To solve question 2: Question 2
To read the article: Application of Average Speed in Distance problems
To solve question 2: Question 2
To read the article: Application of Average Speed in Distance problems
09 May 2018, 08:32
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Solution
Given:
• A straight highway connects two cities P and Q, and goes via two checkpoints M and N, in that order
• A bus started from P and moved to M at an average speed of 30 mph
• After crossing M, it increased its speed to 50 mph, towards N
• From N, it further increased its speed to 60 mph till it reached Q
To find:
• The average speed of the bus throughout the whole journey
Approach and Working:
The given scenario can be depicted using the following table:
Let us assume that the distance between P and M is x, between M and N is y, and between N and Q is z.
Therefore, the average speed of the whole journey = (x + y + z) / (x/30 + y/50 + z/60)
Analysing Statement 1
• As per the information given in Statement 1, the ratio of time the bus took to cover the distances PM, MN, and NQ respectively is 2:1:3
- o Let us assume the time taken for the individual parts of the journey to be 2t, t, and 3t
- o \(\frac{x}{30}\) = 2t or, x = 60t
o \(\frac{y}{50}\) = t or, y = 50t
o \(\frac{z}{60}\) = 3t or, z = 180t
• Therefore, the average speed = total distance travelled/ total time taken
- o Or, average speed = (x + y + z)/(2t + t + 3t) = (60t + 50t + 180t)/6t = \(\frac{290t}{6t} = \frac{145}{3}\) mph
Analysing Statement 2
• As per the information given in Statement 2, out of the three distances, NQ is 3 times the distance PM and more than 3 times the distance MN
- o Given that distance NQ is more than 3 times the distance MN, we cannot get any exact value of MN
Hence, the correct answer is Option A.
Answer: A
22 Jun 2023, 23:34
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EgmatQuantExpert
why we can't take t1=Pm/30, t2=pm/50 and t3=3pm/60. from that we get total time. Total distance is 5pm.so we can calculate average speed..right? hence D
