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Sarah goes from P to Q in a boat and comes back to R which is exactly

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Bunuel
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Sarah goes from P to Q in a boat and comes back to R which is exactly [#permalink] Sarah goes from P to Q in a boat and comes back to R which is exactly   11 Jun 2020, 04:32
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Sarah goes from P to Q in a boat and comes back to R which is exactly in between P and Q in 33 hours. The speed of the boat and the stream is 30km/hr and 20 km/hr respectively. If the river flows uniformly in one direction only, then how much time (in hours) will she take to go downstream from Q to P?

A. 4
B. 5
C. 6
D. 7
E. 8
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C
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Re: Sarah goes from P to Q in a boat and comes back to R which is exactly [#permalink] Sarah goes from P to Q in a boat and comes back to R which is exactly   11 Jun 2020, 04:41
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Speed of boat = 30. = B
Speed of stream = 20. = S
Total time taken to cover 1.5D = 33
The equation will be P to Q is upstream and Q to R is half way downstream = D/(B-S)+(D/2)/(B+S) = 33
=> D/(30-20) + D/2*(30+20) = 33
=> D/10 + D/100 = 33
=> (10D+D)/100 = 33
=> 11D = 3300
=> D = 300

Time to reach downstream = 300/50 (distance/boat speed+stream speed) = 6

Answer is 6

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Re: Sarah goes from P to Q in a boat and comes back to R which is exactly [#permalink] Sarah goes from P to Q in a boat and comes back to R which is exactly   11 Jun 2020, 04:42
D/10 + D/2×50 =33
11D/100 =33
D= 300
T =300/50
= 6hrs
Option C is the answer.

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Re: Sarah goes from P to Q in a boat and comes back to R which is exactly [#permalink] Sarah goes from P to Q in a boat and comes back to R which is exactly   11 Jun 2020, 04:58
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Bunuel
Sarah goes from P to Q in a boat and comes back to R which is exactly in between P and Q in 33 hours. The speed of the boat and the stream is 30km/hr and 20 km/hr respectively. If the river flows uniformly in one direction only, then how much time (in hours) will she take to go downstream from Q to P?

A. 4
B. 5
C. 6
D. 7
E. 8

Solution


    • Let us assume that Sarah takes t hours to go downstream from Q to P and distance between P and Q is d kms.
    • Speed of the boat during its downstream journey (i.e Q to P or Q to R) \(= 30 + 20 = 50\) km/h
    • Speed of the boat during its upstream journey (i.e. P to Q) \(= 30 – 20 = 10 \)km/h
    • Now, time taken by Sarah to go from Q to R \(= \frac{t}{2 }= \frac{d}{2(50)} ⟹ \frac{t}{2} = \frac{d}{100} ….Eq.(i)\)
    • Also, time taken by Sarah to go from P to Q \(= \frac{d}{10} \)
      o From the above equation and Eq.(i), we can write,
         time taken by boat to go from P to Q \(= \frac{d}{10 }= 5t\)
    • Now, \(5t + \frac{t}{2} = 33 ⟹ 11t = 2*33 ⟹ t = 6 \)hours.
Thus, the correct answer is Option C.
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Re: Sarah goes from P to Q in a boat and comes back to R which is exactly [#permalink] Sarah goes from P to Q in a boat and comes back to R which is exactly   11 Jun 2020, 08:51
Bunuel
Sarah goes from P to Q in a boat and comes back to R which is exactly in between P and Q in 33 hours. The speed of the boat and the stream is 30km/hr and 20 km/hr respectively. If the river flows uniformly in one direction only, then how much time (in hours) will she take to go downstream from Q to P?

A. 4
B. 5
C. 6
D. 7
E. 8

total time= 33hrs
let distance p to q =x
given

p----------r----------------q
--- x/2---------------x/2----
speed upstream from p to q = 30-20 ; 10 kmph and downstream = 30+20 ; 50 kmph
net time
x/10+x/100 = 33
solve for x = 300
so time taken from q to p ; 300/50 ; 6 hours
OPTION C
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Re: Sarah goes from P to Q in a boat and comes back to R which is exactly [#permalink] Sarah goes from P to Q in a boat and comes back to R which is exactly   12 Aug 2024, 12:59
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Re: Sarah goes from P to Q in a boat and comes back to R which is exactly [#permalink]
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