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Samia set off on her bicycle to visit her friend, traveling at an aver

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Samia set off on her bicycle to visit her friend, traveling at an aver  [#permalink]

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New post 03 Apr 2019, 04:32
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A
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C
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Difficulty:

  55% (hard)

Question Stats:

65% (02:53) correct 35% (03:00) wrong based on 34 sessions

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Samia set off on her bicycle to visit her friend, traveling at an average speed of 17 kilometers per hour. When she had gone half the distance to her friend’s house, a tire went flat, and she walked the rest of the way at 5 kilometers per hour. In all it took her 44 minutes to reach her friend’s house. In kilometers rounded to the nearest tenth, how far did Samia walk?

(A) 2.0

(B) 2.2

(C) 2.8

(D) 3.4

(E) 4.4

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Samia set off on her bicycle to visit her friend, traveling at an aver  [#permalink]

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New post 03 Apr 2019, 10:48
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Let the total distance traveled by Samia be x.
She traveled half the distance(x/2) by bike at 17kmph and the other half(x/2) by walk at 5kmph.
Time = 44/60 hrs.
Average Speed = Total Distance/Time taken

\(\frac{x}{(x/(2*17)+x/(2*5))}\)

\(\frac{x}{((5x+17x)/170)}\) = \(\frac{170x}{22x}\) = \(\frac{85}{11}\) kmph

Distance, x = \(\frac{85}{11}*\frac{44}{60}\) km = \(\frac{17}{3}\) = Almost 6.

Distance traveled by walk = x/2 = 6/2 = 3.

C is the closest.

C is the answer.
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Re: Samia set off on her bicycle to visit her friend, traveling at an aver  [#permalink]

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New post 04 Apr 2019, 00:25
Let the distance she walks be 'x' kms; so the distance she bikes must also be 'x' kms since she had a flat half-way to her friend's place.
Therefore, she biked for x/17 hrs and walked for x/5 hrs.
So, (x/17 + x/5) hrs = 44 mins = 44/60 hrs
x = 2.83. Ans: C
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Re: Samia set off on her bicycle to visit her friend, traveling at an aver  [#permalink]

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New post 07 Apr 2019, 18:21
Noshad wrote:
Samia set off on her bicycle to visit her friend, traveling at an average speed of 17 kilometers per hour. When she had gone half the distance to her friend’s house, a tire went flat, and she walked the rest of the way at 5 kilometers per hour. In all it took her 44 minutes to reach her friend’s house. In kilometers rounded to the nearest tenth, how far did Samia walk?

(A) 2.0

(B) 2.2

(C) 2.8

(D) 3.4

(E) 4.4


Let d be the distance to Samia’s friend’s house. We can create the equation:

(d/2)/17 + (d/2)/5 = 44/60

d/34 + d/10 = 44/60

10d/340 + 34d/340 = 44/60

44d/340 = 44/60

d/340 = 1/60

60d = 340

d ≈ 5.6

Since she walked only half of the distance from her house to her friend’s house, she walked approximately 2.8 km.

Answer: C
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Re: Samia set off on her bicycle to visit her friend, traveling at an aver  [#permalink]

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New post 08 Apr 2019, 23:10
Hi,

I took 3 minutes to solve this. Is there any easy method to solve this problem in less time?
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Re: Samia set off on her bicycle to visit her friend, traveling at an aver   [#permalink] 08 Apr 2019, 23:10
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Samia set off on her bicycle to visit her friend, traveling at an aver

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