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10 Aug 2022, 01:49
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (03:02) correct
37%
(02:46)
wrong
based on 172
sessions
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Not Attempted Yet
On Sunday, Ron begins to drive due north from point T at a constant rate of x miles per hour. Two hours after Ron started, Sam begins to drive due south from point T at a constant rate of y miles per hour. If y>4x, for how many hours Ron would have driven when Sam had covered thrice as much distance as Ron?
A. x/(x - 2y)
B. 2y/(x - 3y)
C. 2y/(y - 3x)
D. 2x/(x + 4y)
E. 2x/(y - 3x)
A. x/(x - 2y)
B. 2y/(x - 3y)
C. 2y/(y - 3x)
D. 2x/(x + 4y)
E. 2x/(y - 3x)
11 Aug 2022, 19:02
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Aabhash777
Two ways…
(I)
Choose numbers for the variables.
Let x and y be 10 and 50…..50>4*10.
If the time is a, then 3(10*a)=50*(a-2)
30a=50a-100 or a=5.
Look for the option that gives you answer 5.
A and B will have negative denominator, so eliminate.
\(\frac{2y}{(y-3x)}=\frac{2*50}{(50-3*10)}=\frac{100}{20}=5\)
C
(II)
Algebraic
Let the time Ron has traveled be a, so Sam has traveled for a-2 hours.
Distance traveled by Ron is x*a, while Sam travels y(a-2).
Now it is given that \(3(x*a)=y(a-2)……3xa=ay-2y……..ay-3ax=2y………a(y-3x)=2y……..a=\frac{2y}{y-3x}\)
C
12 Aug 2022, 03:17
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Time taken by Ron = t
so Sam time = t-2 hours.
Distance traveled by Ron is x*t, while Sam travels y(t-2).
Now it is given that 3(x∗t)=y(t−2)
3xt=ty−2y
3xt-ty = -2y
ty-3xt = 2y
t(y-3x) = 2y
t= 2y/(y-3x)
so Sam time = t-2 hours.
Distance traveled by Ron is x*t, while Sam travels y(t-2).
Now it is given that 3(x∗t)=y(t−2)
3xt=ty−2y
3xt-ty = -2y
ty-3xt = 2y
t(y-3x) = 2y
t= 2y/(y-3x)
