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Athena walks to work

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by anniev2 » Mon Mar 02, 2009 7:48 am
this is from the rate problems document pulled from the resources section of this site:

Athena always walks to work at a speed of 4 miles per hour, and jogs home along the same route at a speed of 8 miles per hour. If she spends exactly 2 hours total traveling both ways, how far, in miles, is her house from her work?

(A) 2
(B) 4
(C) 16/3
(D) 20/3
(E) 8


Can someone please explain the solution below. I think the 4 in the equation is from the number of hours she walked/jogged since it reads "2 hours total traveling both ways"....does this mean she traveled 2 hours or 4 hours, I can't determine.
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by truplayer256 » Mon Mar 02, 2009 7:57 am
Here's a solution that you may understand. Athena takes x hours to walk to work at a rate of 4 mph. Now if you think about it, it'll only take Athena x/2 hours to actually jog back home since she's going twice the speed that she walks to work. So,

x+x/2=2
x=4/3
It takes Athena 4/3 hours to walk to work at rate of 4 mph. Since we want to find the the distance between her home and work, we do 4(4/3)=16/3 miles
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Re: Athena walks to work

by kamu » Mon Mar 02, 2009 8:04 am
anniev2 wrote:this is from the rate problems document pulled from the resources section of this site:

Athena always walks to work at a speed of 4 miles per hour, and jogs home along the same route at a speed of 8 miles per hour....
notice that the distance covered is same for these two lines.

she spends exactly 2 hours total traveling both ways
not one way!! :)
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by deepoe » Mon Mar 02, 2009 9:08 am
Athena always walks to work at a speed of 4 miles per hour, and jogs home along the same route at a speed of 8 miles per hour. If she spends exactly 2 hours total traveling both ways, how far, in miles, is her house from her work?


x / 4 + x / 8 = 2

2x / 8 + x / 8 = 2

3x / 8 = 2

3x = 16

X = 16 / 3
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by truplayer256 » Mon Mar 02, 2009 9:16 am
Yeah, Deepoe, I think you edited your previous question on how I got the 3 from x+x/2=2. I simply solved for x.
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Re: Athena walks to work

by farooq » Mon Mar 02, 2009 10:10 am
anniev2 wrote:this is from the rate problems document pulled from the resources section of this site:

Athena always walks to work at a speed of 4 miles per hour, and jogs home along the same route at a speed of 8 miles per hour. If she spends exactly 2 hours total traveling both ways, how far, in miles, is her house from her work?

(A) 2
(B) 4
(C) 16/3
(D) 20/3
(E) 8


Can someone please explain the solution below. I think the 4 in the equation is from the number of hours she walked/jogged since it reads "2 hours total traveling both ways"....does this mean she traveled 2 hours or 4 hours, I can't determine.
S1=4m/h
S2=8m/h

Total time = 2 h

Distnace is same.

Therefore, ration of speed is S1:S2=t2:t1

4:8=t2:t1

or we can say t1:t2=8:4.

Now total time is 2 hrs.

So, t1=(8/12)*2 =4/3 (ratio and proportion concept).

Distance = S1*t1 = 4*(4/3)=16/3.
Regards,
Farooq Farooqui.
London. UK

It is your Attitude, not your Aptitude, that determines your Altitude.
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