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18 Jul 2024, 10:20
Kudos
Bookmarks
Let's analyze each statement to determine if it provides sufficient information to find Train A's average speed during the journey from Liverpool to London.
Given Information:
- Distance from Liverpool to London is 300 kilometers.
- Train A reached London when Train B had 80 kilometers left to cover.
- Therefore, Train B had traveled 300 - 80 = 220 kilometers when Train A reached London.
Question:
What was Train A's average speed during this journey?
Analyzing the Statements:
Statement (1):
During the first hour, Train B covered 40 kilometers less than Train A.
Let v_A be Train A's average speed, and v_B be Train B's average speed.
From the information given:
- When Train A reached London, Train B had 80 kilometers left, meaning Train B had traveled 220 kilometers.
- This means that Train B's travel time is the same as Train A's travel time since they departed simultaneously.
From Statement (1):
- If Train A's speed is v_A, it covered v_A kilometers in the first hour.
- Train B covered v_A - 40 kilometers in the first hour.
However, this statement alone does not provide enough information to determine v_A directly. We need more data to link v_A and v_B over the entire journey.
Statement (2):
Train B's average speed for the first 110 kilometers was 110 kilometers per hour.
From Statement (2):
- Train B's average speed for the first 110 kilometers is 110 kilometers per hour.
- This gives us information about Train B's initial speed but not enough about Train B's overall average speed or Train A's speed over the entire journey.
Combining Both Statements:
If we combine both statements:
- From Statement (1), we know Train B's initial speed relative to Train A's initial speed.
- From Statement (2), we know Train B's speed for the first 110 kilometers.
However, combining both statements still does not provide a direct relationship between Train A's overall average speed and the given data points. We do not have a clear link between the entire journey of Train B and its average speed.
IMO E.
Given Information:
- Distance from Liverpool to London is 300 kilometers.
- Train A reached London when Train B had 80 kilometers left to cover.
- Therefore, Train B had traveled 300 - 80 = 220 kilometers when Train A reached London.
Question:
What was Train A's average speed during this journey?
Analyzing the Statements:
Statement (1):
During the first hour, Train B covered 40 kilometers less than Train A.
Let v_A be Train A's average speed, and v_B be Train B's average speed.
From the information given:
- When Train A reached London, Train B had 80 kilometers left, meaning Train B had traveled 220 kilometers.
- This means that Train B's travel time is the same as Train A's travel time since they departed simultaneously.
From Statement (1):
- If Train A's speed is v_A, it covered v_A kilometers in the first hour.
- Train B covered v_A - 40 kilometers in the first hour.
However, this statement alone does not provide enough information to determine v_A directly. We need more data to link v_A and v_B over the entire journey.
Statement (2):
Train B's average speed for the first 110 kilometers was 110 kilometers per hour.
From Statement (2):
- Train B's average speed for the first 110 kilometers is 110 kilometers per hour.
- This gives us information about Train B's initial speed but not enough about Train B's overall average speed or Train A's speed over the entire journey.
Combining Both Statements:
If we combine both statements:
- From Statement (1), we know Train B's initial speed relative to Train A's initial speed.
- From Statement (2), we know Train B's speed for the first 110 kilometers.
However, combining both statements still does not provide a direct relationship between Train A's overall average speed and the given data points. We do not have a clear link between the entire journey of Train B and its average speed.
IMO E.
18 Jul 2024, 10:39
Kudos
Bookmarks
Train A and Train B each departed simultaneously from Liverpool heading to London, which is 300 kilometers away. When Train A reached the destination, Train B still had 80 kilometers left to cover. What was Train A's average speed during this journey?
Spped A/ Speed B= 300/220= 15/11
(1) During the first hour, Train B covered 40 kilometers less than Train A.-- We only have relative speed for first hour and dont know individual speeds for a and b either in the first hour or throughout the journey. Speed in the first hour is 150
NS
(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.-- We only know speed for B for first hour and A too but we dont know about second journey
NS
Combined- No new info
NS
Ans E
Spped A/ Speed B= 300/220= 15/11
(1) During the first hour, Train B covered 40 kilometers less than Train A.-- We only have relative speed for first hour and dont know individual speeds for a and b either in the first hour or throughout the journey. Speed in the first hour is 150
NS
(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.-- We only know speed for B for first hour and A too but we dont know about second journey
NS
Combined- No new info
NS
Ans E
18 Jul 2024, 11:31
Kudos
Bookmarks
Given - Train A and Train B each departed simultaneously from Liverpool heading to London, which is 300 kilometers away. When Train A reached the destination, Train B still had 80 kilometers left to cover.
Assuming avg speeds of Train A and B as a and b kmph respectively and when A completed journey B still had 80 km left to travel.
Means in same time Train A travel 300km and B traveled 220km
Therefore, Their speed ratio,
\(\frac{SpeedA}{SpeedB} = \frac{Distance Covered by A}{Distance Covered by B}\)
\(\frac{a}{b} = \frac{300}{220} = \frac{15}{11}\)
To find - What was Train A's average speed during this journey?
1st - During the first hour, Train B covered 40 kilometers less than Train A.
Distance covered by A in 1Hr = Speed*Time = a*1 = a
Distance covered by B in 1Hr = Speed*Time = b*1 = b
Distance covered by A in 1Hr - Distance covered by B in 1Hr = 40
\(a - b = 40\)
and from given data \(b = a*\frac{11}{15}\)
now,
\(a - a*\frac{11}{15} = 40\)
after solving for a,
\(a = 150 kmph\)
But remember this is applicable only for 1st hour and we wanted to calculate Train A's average speed during this journey so this value we got is not applicable for entire journey as question doesn't says both trains are traveling at constant speed for entire journey.
So this is a trap.
Not sufficient.
2nd - Train B's average speed for the first 110 kilometers was 110 kilometers per hour.
b=110 kmph.
again it is including information about first 1Hr.
Not sufficient.
Even after combining both we still got the data only for first hour and we dont about whether speed is constant or not.
Hence even combining both we will still not be able to get data for whole journey.
So, Answer is E.
Assuming avg speeds of Train A and B as a and b kmph respectively and when A completed journey B still had 80 km left to travel.
Means in same time Train A travel 300km and B traveled 220km
Therefore, Their speed ratio,
\(\frac{SpeedA}{SpeedB} = \frac{Distance Covered by A}{Distance Covered by B}\)
\(\frac{a}{b} = \frac{300}{220} = \frac{15}{11}\)
To find - What was Train A's average speed during this journey?
1st - During the first hour, Train B covered 40 kilometers less than Train A.
Distance covered by A in 1Hr = Speed*Time = a*1 = a
Distance covered by B in 1Hr = Speed*Time = b*1 = b
Distance covered by A in 1Hr - Distance covered by B in 1Hr = 40
\(a - b = 40\)
and from given data \(b = a*\frac{11}{15}\)
now,
\(a - a*\frac{11}{15} = 40\)
after solving for a,
\(a = 150 kmph\)
But remember this is applicable only for 1st hour and we wanted to calculate Train A's average speed during this journey so this value we got is not applicable for entire journey as question doesn't says both trains are traveling at constant speed for entire journey.
So this is a trap.
Not sufficient.
2nd - Train B's average speed for the first 110 kilometers was 110 kilometers per hour.
b=110 kmph.
again it is including information about first 1Hr.
Not sufficient.
Even after combining both we still got the data only for first hour and we dont about whether speed is constant or not.
Hence even combining both we will still not be able to get data for whole journey.
So, Answer is E.
