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# Sam drove at a constant speed from inn A along a highway to inn B.

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Sam drove at a constant speed from inn A along a highway to inn B.  [#permalink]

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08 Apr 2019, 11:27
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Difficulty:

65% (hard)

Question Stats:

55% (02:41) correct 45% (01:53) wrong based on 31 sessions

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Sam drove at a constant speed from City X along a highway to City Y. Did Sam reach City Y from City X in less than an hour?

(1) If Sam had driven at the same speed to City Z that was 15 kilometers further down the highway, he would have taken 50% more time

(2) If Sam's average speed for the drive had been 20 kilometers per hour lesser, he would have taken 50% more time

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Sam drove at a constant speed from inn A along a highway to inn B.  [#permalink]

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18 Apr 2019, 07:57
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1
Sam drove at a constant speed from City X along a highway to City Y. Did Sam reach City Y from City X in less than an hour?

Question: is T<1 hours??
Solution: The question uses the same unit for distance, time and speed so no conversion is required.

1) If Sam had driven at the same speed to City Z that was 15 kilometers further down the highway, he would have taken 50% more time

X----T-----Y---(50%T)---Z

$$Speed1 = \frac{distance}{time} = \frac{d}{t}$$

$$Speed2 = \frac{d+15}{1.5t}$$

$$Speed1= speed 2 = \frac{d}{t} = \frac{d+15}{1.5t} => d+15 = 1.5d => 15=0.5d => d=30 Km$$

Speed and time are unknown, Not sufficient

(2) If Sam's average speed for the drive had been 20 kilometers per hour lesser, he would have taken 50% more time

$$Distance1 = Speed*Time = (S)T$$
$$Distance2 = Speed*Time = (S-20)(1.5)T$$
$$Distance1 = Distance2 = ST = (S-20)(1.5)T => S=(S-20)(1.5) => S=60 Km/hr$$

Only speed is available, distance and time are not... if the distance is more than 60 then time is greater than 1 hour, less than 60 time is less than 1 hour. Not sufficient

Using 1 and 2
From 1: distance=30 Km
From 2: Speed = 60 Km/Hour

$$Time = \frac{Distance}{Speed} = \frac{30}{60}=\frac{1}{2}hour$$ = 30 mins < 1 hour sufficient. C
Sam drove at a constant speed from inn A along a highway to inn B.   [#permalink] 18 Apr 2019, 07:57
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# Sam drove at a constant speed from inn A along a highway to inn B.

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