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23 Jan 2018, 23:45
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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% (03:03) correct
31%
(03:05)
wrong
based on 181
sessions
History
Date
Time
Result
Not Attempted Yet
Radina and Russell are participating the Greystone Annual Run/Walk. Radina leaves a half hour after Russell and runs 1 mile per hour slower than twice Russell's rate. If Radina arrives at the finish line 4 hours after she started and finishes at the same time as Russell, approximately how many miles long is the race?
A. 4/3
B. 7/2
C. 9/2
D. 32/7
E. 36/7
A. 4/3
B. 7/2
C. 9/2
D. 32/7
E. 36/7
24 Jan 2018, 10:34
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Speed of Russell = s
Speed of Radina = 2s - 1
Time taken by Radina = 4 hrs
Time taken by Russell = 4.5 hrs
(2s - 1)*4 = s * 4.5
s = 8/7
Distance = s * 4.5 = (8/7) * (9/2) = 36/7
Answer: E
Speed of Radina = 2s - 1
Time taken by Radina = 4 hrs
Time taken by Russell = 4.5 hrs
(2s - 1)*4 = s * 4.5
s = 8/7
Distance = s * 4.5 = (8/7) * (9/2) = 36/7
Answer: E
24 Jan 2018, 17:22
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Bunuel
Set up (R*T) = D for each runner. Set distances equal to each other, which will yield one actual rate. Use that rate to find distance.
1) TIME for each runner
Radina: 4 hours
Russell: 30 minutes MORE:\(4\frac{1}{2}=\frac{9}{2}\) hours
2) RATE for each in variables
Let Russell's rate = R
Radina's rate = (2R - 1)
3) Find Russell's actual rate from D = D (they run the same distance)
\((2R - 1)(4) = (R)(\frac{9}{2})\)
\((2R - 1)(8) = 9R\)
\(16R - 8 = 9R\)
\(7R = 8\)
\(R = \frac{8}{7}\) mph
4) Actual distance?
Use Russell's rate * time:
\(D = (\frac{8}{7}mph * \frac{9}{2}hrs) = \frac{36}{7}\) miles
Answer E
If D = \(\frac{36}{7}\), then Radina's rate is D/T: \(\frac{\frac{36}{7}}{4} = \frac{36}{28} = \frac{9}{7}\)
Radina's rate is also (2R - 1)
Radina's rate: \([(\frac{8}{7}*2) - 1] = (\frac{16}{7} - \frac{7}{7}) = \frac{9}{7}\)
That's a match. The answer is correct.
