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19 Jul 2021, 21:00
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Roger: 50 miles/hour
Kelly: 75 miles/hour
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:
77% (02:47) correct
23%
(02:57)
wrong
based on 875
sessions
History
Date
Time
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Not Attempted Yet
Roger and Kelly are going on a road trip. If Roger drives at his normal rate of speed for the first 4 hours, then Kelly can drive the remaining distance in 4 more hours. If, however, Roger drives 75% faster than normal for 4 hours, Kelly can drive the remaining distance at her regular rate of speed in 2 hours.
In the table below, choose a normal rate of speed for Roger and a normal rate of speed for Kelly that are consistent with the information above.
In the table below, choose a normal rate of speed for Roger and a normal rate of speed for Kelly that are consistent with the information above.
| Roger | Kelly | |
| 50 miles/hour | ||
| 55 miles/hour | ||
| 60 miles/hour | ||
| 65 miles/hour | ||
| 70 miles/hour | ||
| 75 miles/hour |
ShowHide Answer
Official Answer
Roger: 50 miles/hour
Kelly: 75 miles/hour
24 Mar 2022, 03:24
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Normal Condition
X = Speed of Roger
Y = Speed of Kelly
Speed = Distance/Time
Therefore, Distance = Speed * Time
X*4+Y*4 = Distance = 4(X+Y)
New Condition
Speed of Roger = \(\frac{175}{100}\) X = \(\frac{7}{4}\) X
Speed of Kelly = Y
\(\frac{7}{4}\) X * 4 + Y*2 = 4(X+Y)
7X + 2Y = 4X + 4Y
7X-4X + 2Y-4Y = 0
3X - 2Y = 0
From the given option, X=50 & Y=75 are the only options that can satisfy 3X - 2Y = 0
Answer
Roger = 50 miles/hour
Kelly = 75 miles/hour
X = Speed of Roger
Y = Speed of Kelly
Speed = Distance/Time
Therefore, Distance = Speed * Time
X*4+Y*4 = Distance = 4(X+Y)
New Condition
Speed of Roger = \(\frac{175}{100}\) X = \(\frac{7}{4}\) X
Speed of Kelly = Y
\(\frac{7}{4}\) X * 4 + Y*2 = 4(X+Y)
7X + 2Y = 4X + 4Y
7X-4X + 2Y-4Y = 0
3X - 2Y = 0
From the given option, X=50 & Y=75 are the only options that can satisfy 3X - 2Y = 0
Answer
Roger = 50 miles/hour
Kelly = 75 miles/hour
General Discussion
19 Sep 2024, 11:27
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Lets assume x and y are speeds of roger and Kelly respectively.
75% faster means, Roger covers 0.75X more distance per hour.
In four hours roger covers 0.75X *4 = 3X, which helps Kelly to drive 2 hours less, = 2*Y
so 3X=2Y..
X=50 and Y = 75. fits from options.
75% faster means, Roger covers 0.75X more distance per hour.
In four hours roger covers 0.75X *4 = 3X, which helps Kelly to drive 2 hours less, = 2*Y
so 3X=2Y..
X=50 and Y = 75. fits from options.
