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# Jack traveled from Town X to Town Y in 3 hours, and her speed was betw

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
Jack traveled from Town X to Town Y in 3 hours, and her speed was betw  [#permalink]

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04 Oct 2018, 01:57
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Difficulty:

15% (low)

Question Stats:

89% (02:00) correct 11% (02:02) wrong based on 71 sessions

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Jack traveled from Town X to Town Y in 3 hours, and her speed was between 30 miles per hour and 45 miles per hour. Brian also traveled from Town X to Town Y along the same route in 2 hours, and his speed was between 35 miles per hour and 55 miles per hour. Which of the following could be the distance, in miles, from Town X to Town Y?

(A) 8
(B) 105
(C) 115
(D) 120
(E) 135

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Jack traveled from Town X to Town Y in 3 hours, and her speed was betw  [#permalink]

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04 Oct 2018, 03:00
If we take jack’s speed to be 30 or 45 we get distance = 3 * 30 = 90 miles
Or 3*45 = 135 miles

His speed is between 30 and 45 so the distance must be between these two values.

For brian if we do the same case 35 or 55

35 * 2 = 70
55 * 2 = 110

Brian’s distance is 70 < x < 110

Jack’s distance is 90 < y < 135

The only distance that overlaps between the two is 105

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Re: Jack traveled from Town X to Town Y in 3 hours, and her speed was betw  [#permalink]

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05 Oct 2018, 18:38
Bunuel wrote:
Jack traveled from Town X to Town Y in 3 hours, and her speed was between 30 miles per hour and 45 miles per hour. Brian also traveled from Town X to Town Y along the same route in 2 hours, and his speed was between 35 miles per hour and 55 miles per hour. Which of the following could be the distance, in miles, from Town X to Town Y?

(A) 8
(B) 105
(C) 115
(D) 120
(E) 135

I tried with the backsolving approach.
Of the answer choices given,let's assume that 115 could be a possible distance. So as per the question stem,Jack's speed would be 115/3 = 38.33mph which falls into the bracket given in the question. But Brian's speed would be 115/2 = 57.5mph which exceeds the given bracket. Going anything above 115 would make no sense as the speeds for the two of them would be too high. So we go to try with answer choice B,i.e.105. With 105,Jack's speed would be 35mph and Brian's speed would be 52.5mph,both of which satisfy the bracket. Hence,B is the correct choice.
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Re: Jack traveled from Town X to Town Y in 3 hours, and her speed was betw  [#permalink]

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09 Oct 2018, 10:42
Bunuel wrote:
Jack traveled from Town X to Town Y in 3 hours, and her speed was between 30 miles per hour and 45 miles per hour. Brian also traveled from Town X to Town Y along the same route in 2 hours, and his speed was between 35 miles per hour and 55 miles per hour. Which of the following could be the distance, in miles, from Town X to Town Y?

(A) 8
(B) 105
(C) 115
(D) 120
(E) 135

Using Jack’s speed, the distance between Town X and Town Y ranges between:

30 x 3 = 90 miles and 45 x 3 = 135 miles

Using Brian’s speed, the distance between Town X and Town Y ranges between:

35 x 2 = 70 miles and 55 x 2 = 110 miles

Thus, a possible distance is 105 miles.

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Re: Jack traveled from Town X to Town Y in 3 hours, and her speed was betw   [#permalink] 09 Oct 2018, 10:42
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