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# It takes Kaya a total of 9 hours to go from home to work and back on

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Math Expert
Joined: 02 Sep 2009
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It takes Kaya a total of 9 hours to go from home to work and back on  [#permalink]

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28 Apr 2017, 02:17
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Difficulty:

25% (medium)

Question Stats:

77% (01:58) correct 23% (02:25) wrong based on 265 sessions

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It takes Kaya a total of 9 hours to go from home to work and back on her bike. She travels at an average speed of 5 miles per hour from home to work and twice as fast coming home than going to work. If Kaya travels by the same route in both directions then how many miles is the distance from her home to work?

A. 67.5
B. 45
C. 30
D. 18
E. 6

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It takes Kaya a total of 9 hours to go from home to work and back on  [#permalink]

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28 Apr 2017, 02:46
1
Let the time taken for one leg of the jouney be x
Hence, time taken for other leg is 9-x
Speed for the legs are given to be 5 and 10 respectively
Since distance covered is the same in both the legs

Formula used : Distance = Speed * Time

10(x) = 5(9-x)
x=3

Distance traveled one way is 3x which is 30(Option C)
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It takes Kaya a total of 9 hours to go from home to work and back on  [#permalink]

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28 Apr 2017, 03:29
Speed ratio 1:2
So Time ratio 2:1
That is 6hours : 3 hours

distance = speed * time

Home to work dist= 5miles/hr *6hrs =30miles

Option C

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Director
Joined: 21 Mar 2016
Posts: 522
Re: It takes Kaya a total of 9 hours to go from home to work and back on  [#permalink]

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02 May 2017, 03:45
can be solved using ratio,,

speed ratio is 5:10 or 1:2
time ratio will be 2:1.. in a total of 9 hours,,
6 hours for going and 3 hours for coming back,,

distance = 5* 6 = 30

ans C
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It takes Kaya a total of 9 hours to go from home to work and back on  [#permalink]

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02 May 2017, 08:26
Bunuel wrote:
It takes Kaya a total of 9 hours to go from home to work and back on her bike. She travels at an average speed of 5 miles per hour from home to work and twice as fast coming home than going to work. If Kaya travels by the same route in both directions then how many miles is the distance from her home to work?

A. 67.5
B. 45
C. 30
D. 18
E. 6

as K's speed ratio going/returning is 5:10, or 1:2,
her time ratio going/returning is 2:1, or 6:3
5 mph*6 hrs=30 miles distance
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Joined: 14 May 2015
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Re: It takes Kaya a total of 9 hours to go from home to work and back on  [#permalink]

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02 May 2017, 14:39
home to office speed=5 kmph
office to home speed= 5*2= 10 kmph
Time=Distance/speed
D/5 + D/10 = 9
D= 30
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Re: It takes Kaya a total of 9 hours to go from home to work and back on  [#permalink]

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02 May 2017, 15:50
1
Bunuel wrote:
It takes Kaya a total of 9 hours to go from home to work and back on her bike. She travels at an average speed of 5 miles per hour from home to work and twice as fast coming home than going to work. If Kaya travels by the same route in both directions then how many miles is the distance from her home to work?

A. 67.5
B. 45
C. 30
D. 18
E. 6

We are given that Kaya takes a total of 9 hours to make the round trip from home to work and back home. She has a rate of 5 mph when going from home to work, and her rate is twice as fast when coming home, so 10 mph.

If we let the distance between home and work = d, then her time from home to work is d/5 and her time from work to home is d/10. Since the total time is 9 hours, we can create the following equation to determine d:

d/5 + d/10 = 9

Multiplying the entire equation by 10, we have:

2d + d = 90

3d = 90

d = 30

Alternate Solution:

Let’s denote the time it takes Kaya to go back home from work as t. Since Kaya travels twice as fast going home, the time it takes for her to go to work is twice as long as the time to go home, i.e. 2t. We are given that the total time is 9 hours, thus t + 2t = 3t = 9 and t = 3. Since it takes 2t = 6 hours at 5 mph to go to work, the distance is 6 x 5 = 30 miles.

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Joined: 01 Jan 2016
Posts: 28
Re: It takes Kaya a total of 9 hours to go from home to work and back on  [#permalink]

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21 May 2017, 17:43
Bunuel wrote:
It takes Kaya a total of 9 hours to go from home to work and back on her bike. She travels at an average speed of 5 miles per hour from home to work and twice as fast coming home than going to work. If Kaya travels by the same route in both directions then how many miles is the distance from her home to work?

A. 67.5
B. 45
C. 30
D. 18
E. 6

Avg speed formula = 2s1s2/s1+s2

D = 20/3 * 9
D=3
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Re: It takes Kaya a total of 9 hours to go from home to work and back on  [#permalink]

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08 Jun 2017, 02:55
D/9 = D/(D/5 + D/10)

10/3 = D/9

D = 90/3 ----> 30
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Re: It takes Kaya a total of 9 hours to go from home to work and back on  [#permalink]

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21 Sep 2018, 22:41
Quote:
It takes Kaya a total of 9 hours to go from home to work and back on her bike. She travels at an average speed of 5 miles per hour from home to work and twice as fast coming home than going to work. If Kaya travels by the same route in both directions then how many miles is the distance from her home to work?

A. 67.5
B. 45
C. 30
D. 18
E. 6

Let the distance between home and office be 'x' miles

Time = $$\frac{Distance}{Speed}$$

Speed at which she travels from home to office = 5 mph
Speed at which she travels from office to home = 10 mph

Time taken = 9hrs = $$\frac{x}{5}$$ +$$\frac{x}{10}$$

x = 30 miles
Re: It takes Kaya a total of 9 hours to go from home to work and back on &nbs [#permalink] 21 Sep 2018, 22:41
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