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

Question

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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tgsankar10 · Answer

Total time taken  = 44 	ext{mins}

Distance traveled by both modes are equal

17c=5w

\frac{c}{w}=\frac{5}{17} , They both constitue 22 parts total, which is half the total time taken. Hence:

\frac{c}{w}=\frac{10}{34}

Distance walked  =5w=\frac{5*34}{60}=\frac{170}{60}= 	ext{little less than 3}

Answer is C

Krunaal · Answer

Travelling by bicycle

Average Speed = 17 kmph
Distance travelled = D/2 (Let D be overall distance)
Time travelled = D/34 (Distance travelled/Average Speed)..............(1)

Walking

Average Speed = 5 kmph
Distance travelled = D/2 (Let D be overall distance)
Time travelled = D/10 (Distance travelled/Average Speed)................(2)

Overall

Time travelled = 44 mins => 44/60 hours => 11/15 hours
Distance travelled = D
Average Speed = 15D/11 (Distance travelled/Time travelled)...............(3)

Now, Average Speed is also equal to Total Distance / Total Time

15D/11 = D / (D/34 + D/10).....................(from 1, 2, and 3)
Solving we get, D = 34/6
We need Distance spent walking i.e. D/2 => 34/12 => 17/6 => 2.83 kms
Rounded to nearest tenth, 2.8 kms

100percentileman · Answer

It states that Samia cycled half the distance and walked the second half.
Let the total distance be X.
Let the time she cycled be t1 and the time she walked be t2.
t1 +t2 = 44/60 hrs ---------1

Since her average speed while cycling was 17,
17 = (x/2)/ t1 --> t1 = x/34
Since her average walking speed was 5,
5 = (x/2)/ t2 --> t2 = x/10

plug the values into 1,

x/34 + x/10 = 44/60
=> 22x/85 = 44/30
=> x= (44/22)*(85/30)
=> x= 85/15 = 5.6
=> x/2 = 2.8

Nidzo · Answer

1st Part of Samia's Trip:

Distance :  x ,  Speed :  17   &  Time :  \frac{x}{17}

2nd Part of Samia's Trip:

Distance :  x  ,  Speed :  5   &  Time :  \frac{x}{5}

Distance Samia covered Walking:   Given that the question asks for a rounded answer and looking at the two times of  \frac{x}{17}  and  \frac{x}{5} ​​​​​​​, let  \frac{x}{17}  be  \frac{x}{15}  to streamline things.

Solving for x by adding the times and making them equal to 44 minutes :  \frac{x}{5} + \frac{x}{15} = \frac{44}{60}

\frac{4x}{15} = \frac{11}{15}

x = \frac{11*15}{15*4}

x = \frac{11}{4}

x ≈ 2.8

ANSWER C

mcrea · Answer

I calculated the average speed as: 2D/(D/17 + D/5) = 85/11
Now, since total distance = total time*average speed, but we just need half the distance, then 85/11 * 3/4 * 1/2 = 2.89

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