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26 May 2017, 11:43
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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:
55%
(hard)
Question Stats:
69% (02:37) correct
31%
(02:56)
wrong
based on 265
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Two gardeners, Burton and Philip, work at independent constant rates to prune a garden full of roses. If both gardeners start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Philip were to work at twice Burton’s rate, they would take only 20 minutes. How long would it take Philip, working alone at his normal rate, to tune the garden full of roses?
A. 1 hour 20 minutes
B. 1 hour 45 minutes
C. 2 hours
D. 2 hours 20 minutes
E. 3 hours
A. 1 hour 20 minutes
B. 1 hour 45 minutes
C. 2 hours
D. 2 hours 20 minutes
E. 3 hours
26 May 2017, 14:16
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Let the rate of work of Burton be x and rate of work(Philip) is y
45(x+y) = 900 units(which we are assuming as the total units of work to be done) ---> eqn1
Also, 20(2x + x) = 900 units of work
(If Philip works at twice Burton’s rate, they would take only 20 minutes)
20(3x) = 900
x = 15 units/minute(Burton's rate)
Substituting x=15 in eqn1, we get 45*(15 + y ) = 900
or y = 5 units/minute, which is the rate of Philip's work.
Hence, time take for Burton to complete the work is 900/5 =180 minutes(Option E)
45(x+y) = 900 units(which we are assuming as the total units of work to be done) ---> eqn1
Also, 20(2x + x) = 900 units of work
(If Philip works at twice Burton’s rate, they would take only 20 minutes)
20(3x) = 900
x = 15 units/minute(Burton's rate)
Substituting x=15 in eqn1, we get 45*(15 + y ) = 900
or y = 5 units/minute, which is the rate of Philip's work.
Hence, time take for Burton to complete the work is 900/5 =180 minutes(Option E)
16 Sep 2018, 19:47
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Quote:
Prune a garden full of roses = 1 job
Burton takes (say) 2x minutes to do 1 job alone.
If Philip takes x minutes to do 1 job alone (to work at twice Burton’s rate), together they would do the job in 20min, hence:
\(\frac{1}{{20}} = \frac{1}{{2x}} + \frac{{1 \cdot \boxed2}}{{x \cdot \boxed2}} = \frac{3}{{2x}}\,\,\,\,\, \Rightarrow \,\,\,x = 30\,\,\,\left[ {\min } \right]\)
Conclusion: Burton takes 2x = 60 minutes to do this job alone.
If Philip takes y minutes to do 1 job alone (our FOCUS!), from the fact that together they would do it in 45min, we have:
\(\frac{1}{{45}} = \frac{1}{{60}} + \frac{1}{y}\,\,\,\,\, \Rightarrow \,\,\,\frac{1}{y} = \frac{{1 \cdot \boxed4}}{{3 \cdot 15 \cdot \boxed4}} - \frac{{1 \cdot \boxed3}}{{4 \cdot 15 \cdot \boxed3}} = \,\,\frac{1}{{3 \cdot 4 \cdot 15}}\,\,\,\,\left[ {\frac{1}{{\min }}} \right]\)
\(? = y = 3 \cdot 60\,\,\min = 3{\text{h}}\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
