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02 Feb 2021, 07:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
61% (03:03) correct
39%
(03:13)
wrong
based on 138
sessions
History
Date
Time
Result
Not Attempted Yet
A boat takes 35 minutes less to travel 28 km downstream than it takes to travel the same distance upstream. If the speed of the boat in still water is 14kmph, what is the speed of the stream ? (in kmph)
(A) 10
(B) 8
(C) 6
(D) 4
(E) 2
(A) 10
(B) 8
(C) 6
(D) 4
(E) 2
03 Feb 2021, 21:18
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\(T_1 =\frac{28}{14-W}\)
\(T_2=\frac{28}{14+W}\)
\(T_1-T_2=\frac{35}{60}\)
\(\frac{28}{14-W} - \frac{28}{14+W} = \frac{35}{60}\) In this stage try to plug in the numbers (or POE) and get the answer quickly
\(\frac{1}{14-W} - \frac{1}{14+W} = \frac{35}{60*28}=\frac{1}{48}\)
\(\frac{14+W-(14-W)}{(14^2-W^2)}=\frac{1}{48}\)
\(48*2W=196-W^2\)
\(W^2+96W-196=0\)
\(W^2+98W-2W-196=0\)
\((W+98)(W-2)=0\)
\(W=2,-98\)
Ans E
\(T_2=\frac{28}{14+W}\)
\(T_1-T_2=\frac{35}{60}\)
\(\frac{28}{14-W} - \frac{28}{14+W} = \frac{35}{60}\) In this stage try to plug in the numbers (or POE) and get the answer quickly
\(\frac{1}{14-W} - \frac{1}{14+W} = \frac{35}{60*28}=\frac{1}{48}\)
\(\frac{14+W-(14-W)}{(14^2-W^2)}=\frac{1}{48}\)
\(48*2W=196-W^2\)
\(W^2+96W-196=0\)
\(W^2+98W-2W-196=0\)
\((W+98)(W-2)=0\)
\(W=2,-98\)
Ans E
13 Feb 2021, 07:14
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Bunuel
Solution:
Letting r be the speed of the stream in kmph and t be the time, in hours, for the boat to travel upstream, we can create the equations:
(14 - r) * t = 28
and
(14 + r) * (t - 35/60) = 28
From the first equation, we see that t = 28 / (14 - r). Substituting this into the second equation, we have:
(14 + r) * (28 / (14 - r) - 7/12) = 28
Multiplying the equation by 12(14 - r), we have:
(14 + r) *[(28 * 12 - 7(14 - r)] = 28 * 12(14 - r)
Dividing the equation by 7, we have:
(14 + r) * (4 * 12 - (14 - r)) = 4 * 12(14 - r)
(14 + r)(34 + r) = 48(14 - r)
476 + 48r + r^2 = 672 - 48r
r^2 + 96r - 196 = 0
(r - 2)(r + 98) = 0
r = 2 or r = -98
Since r can’t be negative, r = 2.
Answer: E
