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03 Feb 2023, 12:15
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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:
85%
(hard)
Question Stats:
60% (03:22) correct
40%
(03:40)
wrong
based on 115
sessions
History
Date
Time
Result
Not Attempted Yet
A man starts rowing from Point A in the direction of the water flow at a constant speed of 10 kilometers per hour. After rowing for 10 kilometers, he remembers that he forgot an important object at Point A and turns back to get it. After getting the object, he starts moving again in the direction of water flow, but due to an onset of exhaustion, he now rows at a constant speed of 8 kilometers per hour. After rowing for 26 kilometers, he reaches Point D, where he rests for 1 hour, and then resumes his journey in the same direction, rowing at a constant speed of 9 kilometers per hour, till he reaches Point B, which is 14 kilometers downstream from Point D. If the speed of water flow is 5 kilometers per hour, what is the average speed of the man for the entire journey?
(A) 9 kilometers per hour
(B) 130/17 kilometers per hour
(C) 120/17 kilometers per hour
(D) 20/3 kilometers per hour
(E) 6 kilometers per hour
(A) 9 kilometers per hour
(B) 130/17 kilometers per hour
(C) 120/17 kilometers per hour
(D) 20/3 kilometers per hour
(E) 6 kilometers per hour
Bunuel
First \(10\) Km's , time taken \(= \frac{10}{10+5} = \frac{10}{15}\)
Return \(10 \) Km's \(= \frac{10}{10-5} =2\)
Next \(26\) Km's \(= \frac{26}{8+5}= 2\)
Rest time \(= 1 \)
Next \(14\) Km's \(= \frac{14}{9+5}= 1\)
Total time \(= \frac{2}{3}+2+2+1+1 = \frac{20}{3}\)
Avg speed = Total distance/ Total time \(= \frac{180}{20} =9\)
Ans A
Hope it helped.
Updated on: 13 Feb 2023, 22:26
Originally posted by SaquibHGMATWhiz on 13 Feb 2023, 11:10.
Last edited by SaquibHGMATWhiz on 13 Feb 2023, 22:26, edited 1 time in total.
Last edited by SaquibHGMATWhiz on 13 Feb 2023, 22:26, edited 1 time in total.
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Bunuel
Solution:
- A to Realization Point (downstream)
- Speed \(10+5=15\) kmph
- Distance \(=10\) km
- Time \(=\frac{Distance}{Time}=\frac{10}{15}=\frac{2}{3}\) hr
- Realization Point to A (upstream)
- Speed \(10-5=5\) kmph
- Distance \(=10\) km
- Time \(=\frac{Distance}{Time}=\frac{10}{5}=2\) hr
- A to D (downstream)
- Speed \(8+5=13\) kmph
- Distance \(=26\) km
- Time \(=\frac{Distance}{Time}=\frac{26}{13}=2\) hr
- Rest time \(=1\) hr
- D to B (downstream)
- Speed \(9+5=14\) kmph
- Distance \(=14\) km
- Time \(=\frac{Distance}{Time}=\frac{14}{14}=1\) hr
- Total distance \(=10+10+26+14=60\) km
- Total time \(=\frac{2}{3}+2+2+1+1=\frac{20}{3}\) hrs
- Average speed \(=\frac{Total_Distance}{Total_Time}=\frac{60}{\frac{20}{3}}=9\)
Hence the right answer is Option A
