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Two brothers, A and B, set out for a station 9 miles away from their 27 Jun 2024, 03:31
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

Question Stats:

73% (02:58) correct 27% (02:52) wrong based on 184 sessions

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­Two brothers, A and B, set out for a station 9 miles away from their home. They both walk at 3 miles per hour. After going one mile, A decided to return to their home for an urgent work. At what rate (in miles per hour) must A now walk in order that he reaches the station at the same time as B, given that he spends 30 minutes at his home?

A. 7/2
B. 15/4
C. 60/13
D. 16 
E. 6­
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C
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whatsarc
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Two brothers, A and B, set out for a station 9 miles away from their 27 Jun 2024, 09:31
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B takes 3 hrs to cover 9 miles.

So total time A can take is also 3hrs.
First 20mins A travels 1 mile.
Now the effective distance A has to cover is 10miles (9+1)
And time left is 2hrs 40mins
But A spends 30more mins at home.
So, time left is 2 hrs and 10mins = 13/6 hrs

Now A has to cover 10mils in 13/6hrs

10/13/6
=60/13­
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Purnank
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Two brothers, A and B, set out for a station 9 miles away from their 27 Jun 2024, 07:42
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Given - Two brothers, A and B, set out for a station 9 miles away from their home. They both walk at 3 miles per hour. After going one mile, A decided to return to their home for an urgent work.
­House ------(1mile)-------(Point of A returning and B heading towards station)-------(8mile)-------Station.
Time taken by B to reach station = Distance / Speed = 8/3 = 2+2/3 (2Hr40Min)
But, A now walk in order that he reaches the station at the same time as B, given that he spends 30 minutes at his home.
Therefore A has to reach station within 2Hr10Min = 13/6Hrs Plus he has to cover 10miles
So, Speed at which A will walk = Distance / Time = 10 / (13/6) = 60/13 mph
Answer C
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Two brothers, A and B, set out for a station 9 miles away from their 27 Jun 2024, 09:43
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riteshrr
B takes 3 hrs to cover 9 miles.

So total time A can take is also 3hrs.
First 20mins A travels 1 mile.
Now the effective distance A has to cover is 10miles (9+1)
And time left is 2hrs 40mins
But A spends 30more mins at home.
So, time left is 2 hrs and 10mins = 13/6 hrs

Now A has to cover 10mils in 13/6hrs

10/13/6
=60/13­
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­I am a bit confused about the way the question is written. It sounds to me like A walks 1 mile at 3mph, returns 1 mile at 3mph, waits 30 minutes and then starts walking at an accelerated rate to catch up to B. Why is it not (110/60)*3 mph? (A walking 9 miles in 110 minutes)
 
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Two brothers, A and B, set out for a station 9 miles away from their 27 Jun 2024, 10:01
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Thisorthat

riteshrr
B takes 3 hrs to cover 9 miles.

So total time A can take is also 3hrs.
First 20mins A travels 1 mile.
Now the effective distance A has to cover is 10miles (9+1)
And time left is 2hrs 40mins
But A spends 30more mins at home.
So, time left is 2 hrs and 10mins = 13/6 hrs

Now A has to cover 10mils in 13/6hrs

10/13/6
=60/13­
­I am a bit confused about the way the question is written. It sounds to me like A walks 1 mile at 3mph, returns 1 mile at 3mph, waits 30 minutes and then starts walking at an accelerated rate to catch up to B. Why is it not (110/60)*3 mph? (A walking 9 miles in 110 minutes)

 
Show more
­

"returns 1 mile at 3mph" is an assumption you are making
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Two brothers, A and B, set out for a station 9 miles away from their 27 Jun 2024, 10:06
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riteshrr

Thisorthat

riteshrr
B takes 3 hrs to cover 9 miles.

So total time A can take is also 3hrs.
First 20mins A travels 1 mile.
Now the effective distance A has to cover is 10miles (9+1)
And time left is 2hrs 40mins
But A spends 30more mins at home.
So, time left is 2 hrs and 10mins = 13/6 hrs

Now A has to cover 10mils in 13/6hrs

10/13/6
=60/13­
­I am a bit confused about the way the question is written. It sounds to me like A walks 1 mile at 3mph, returns 1 mile at 3mph, waits 30 minutes and then starts walking at an accelerated rate to catch up to B. Why is it not (110/60)*3 mph? (A walking 9 miles in 110 minutes)


 
­

"returns 1 mile at 3mph" is an assumption you are making
Show more
­I kind of understand what you mean, but the question says walks 1 mile, 1 mile back and now how fast does it have to walk. The now would imply after 2 miles have been walked, not after 1. You are right since that is the answer choice, but the wording of the question seems dubious/poor
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RaahiK
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Two brothers, A and B, set out for a station 9 miles away from their 21 Aug 2026, 03:17
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you counted the extra 1 mile in the distance but did NOT count the 20 minutes required to walk that 1 mile.
That's inconsistent.
The timeline should be:
20 min → 1 mile out
20 min → 1 mile back
30 min → at home
110 min → 9 miles to station

B takes 9/3 = 3 hrs.
A spends:
  • 20 min going 1 mile
  • 20 min returning
  • 30 min at home
So time left = 180−70=110 min = 11/6 hrs.
He still has 9 miles to cover:
Speed = 9/(11/6) = 54/11
whatsarc
B takes 3 hrs to cover 9 miles.

So total time A can take is also 3hrs.
First 20mins A travels 1 mile.
Now the effective distance A has to cover is 10miles (9+1)
And time left is 2hrs 40mins
But A spends 30more mins at home.
So, time left is 2 hrs and 10mins = 13/6 hrs

Now A has to cover 10mils in 13/6hrs

10/13/6
=60/13­
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