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04 Oct 2023, 01:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
50% (02:59) correct
50%
(02:52)
wrong
based on 72
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Alex and Hales started rowing towards one another at constant speeds and met after rowing for an hour. The initial distance between Alex and Hales was 20 kilometers and Alex rowed downstream while Hales rowed upstream during this journey. On some other day, the time taken by Alex alone, rowing at the same constant speed, to cover the distance between these two points going upstream was 75 minutes more than the time taken by him to cover the same distance going downstream. What was the time taken in hours by Hales to cover 20 kilometers going upstream? Assume the speed of the stream to be 4 kilometers per hour.
A. 1.25
B. 1.6
C. 2.5
D. 5
E. 8
A. 1.25
B. 1.6
C. 2.5
D. 5
E. 8
Updated on: 20 Oct 2023, 21:43
Originally posted by Introvertuprising on 04 Oct 2023, 04:02.
Last edited by Introvertuprising on 20 Oct 2023, 21:43, edited 1 time in total.
Last edited by Introvertuprising on 20 Oct 2023, 21:43, edited 1 time in total.
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Speed of Alex = A
Speed of Hales= H
Distance =20
Speed of the stream =4
They are rowing towards each other and they meet after an hour
Alex rowing downstream then his speed is A+4
Hales rowing upstream then his speed is H+4
Alex and Hales rowing towards each other and meet after an hour
20/(A+4)+(H-4) =1
Alex Downstream takes him T hours
20/A+4 =T
and Upstream takes him T+1.25hrs
20/A-4 =T+1.25
20/A-4 =(20/A+4)+ 1.25
20/(A-4) - 20/(A+4) =1.25
20A+80-20A+80 =1.25(A^2-16)
160/1.25 =A^2-16
128+16 =A^2
Alex speed is 12
20/16+(H-4) =1
20 = 16+H-4
20-12 =H
Hales speed is 8
Hales time taken to go upstream is 20/8-4 =5
Ans D
Speed of Hales= H
Distance =20
Speed of the stream =4
They are rowing towards each other and they meet after an hour
Alex rowing downstream then his speed is A+4
Hales rowing upstream then his speed is H+4
Alex and Hales rowing towards each other and meet after an hour
20/(A+4)+(H-4) =1
Alex Downstream takes him T hours
20/A+4 =T
and Upstream takes him T+1.25hrs
20/A-4 =T+1.25
20/A-4 =(20/A+4)+ 1.25
20/(A-4) - 20/(A+4) =1.25
20A+80-20A+80 =1.25(A^2-16)
160/1.25 =A^2-16
128+16 =A^2
Alex speed is 12
20/16+(H-4) =1
20 = 16+H-4
20-12 =H
Hales speed is 8
Hales time taken to go upstream is 20/8-4 =5
Ans D
04 Oct 2023, 09:57
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Bunuel
I would have solved this question in this way:
We are given that Speed of the stream is 4km/h
Speed Downstream is given by = (u+v) where "u" is the speed of the boat and "v" is the speed of the stream
Speed Upstream is given by = (u-v) where "u" is the speed of the boat and "v" is the speed of the stream
Let Speed of Alex' boat = A
Let Speed of Hales's boat = H
Let Speed of Alex rowing Downstream = A+4
Let Speed of Hales rowing Upstream = H-4
Time when Alex and Hales meet: Initial distance between them/Speed of Alex+Speed of Hales (We are adding the Speed because they are moving towards each other. Similarly, in other cases, we would have deducted the speeds if they were moving away from each other)
We are given that they meet in an hour. We are also given that initial distance between them = 20. So,
1= 20/(A+4)+(H-4)
=>A+H=20
We are also said that Alex rowing at the same speed to cover the same distance going upstream is 75 minutes more than the time taken by him to cover the same distance going downstream.
Alex's Speed Upstream: 20/A-4
Alex's Speed Downstream: 20/A+4
Extra time taken by Alex to row Upstream: 75 minutes which can be written in hours as 75/60 or 5/4
20/A-4 = 20/A+4 + 5/4
This will leave me with A=12
We already know that A+H = 20
Therefore, H = 8 (Which is the speed of Hale's boat)
Time taken in hours by Hales to cover 20 kilometers going upstream: 20/8-4 = 5 hours
Answer is (D)
