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# It takes Mary 30 minutes to walk uphill 1 km from her home to school,

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Math Expert
Joined: 02 Sep 2009
Posts: 59725
It takes Mary 30 minutes to walk uphill 1 km from her home to school,  [#permalink]

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19 Mar 2019, 01:46
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:25) correct 22% (02:07) wrong based on 63 sessions

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It takes Mary 30 minutes to walk uphill 1 km from her home to school, but it takes her only 10 minutes to walk from school to her home along the same route. What is her average speed, in km/hr, for the round trip?

(A) 3
(B) 3.125
(C) 3.5
(D) 4
(E) 4.5

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Re: It takes Mary 30 minutes to walk uphill 1 km from her home to school,  [#permalink]

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19 Mar 2019, 01:58
Bunuel wrote:
It takes Mary 30 minutes to walk uphill 1 km from her home to school, but it takes her only 10 minutes to walk from school to her home along the same route. What is her average speed, in km/hr, for the round trip?

(A) 3
(B) 3.125
(C) 3.5
(D) 4
(E) 4.5

Avg Speed = Total Dist / Total Time

Total Dist = 2 km
Total Time = 3/6 + 1/6 = 4/6 = 2/3

Avg Speed = 2 * 3/2 = 3
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It takes Mary 30 minutes to walk uphill 1 km from her home to school,  [#permalink]

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19 Mar 2019, 02:08
Bunuel wrote:
It takes Mary 30 minutes to walk uphill 1 km from her home to school, but it takes her only 10 minutes to walk from school to her home along the same route. What is her average speed, in km/hr, for the round trip?

(A) 3
(B) 3.125
(C) 3.5
(D) 4
(E) 4.5

Mary takes $$\frac{30}{60}$$ or $$\frac{1}{2}$$ hour to cover the distance uphill.
Mary takes $$\frac{10}{60}$$ or $$\frac{1}{6}$$ hour to cover the same distance downhill

The speeds in km/hr are 2 and 6 km/hr for the to and fro journeys.

Formula(Average speed) = $$\frac{2*a*b}{(a+b)} = \frac{2*2*6}{(2+6)} = \frac{24}{8} = 3$$
Note: This formula works only when the to and fro distances are the same.

Therefore, the average speed for round trip is 3km/hr(Option A)
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Re: It takes Mary 30 minutes to walk uphill 1 km from her home to school,  [#permalink]

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19 Mar 2019, 05:58
Bunuel wrote:
It takes Mary 30 minutes to walk uphill 1 km from her home to school, but it takes her only 10 minutes to walk from school to her home along the same route. What is her average speed, in km/hr, for the round trip?

(A) 3
(B) 3.125
(C) 3.5
(D) 4
(E) 4.5

speed uphill = 30/60 = 1/2 = 2*1 =2 kmph
down hill speed = 10/60 = 1/6 = 1*6 = 6 kmph
avg speed
2*2*6/8 = 3
IMO A
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Re: It takes Mary 30 minutes to walk uphill 1 km from her home to school,  [#permalink]

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21 Mar 2019, 18:05
Bunuel wrote:
It takes Mary 30 minutes to walk uphill 1 km from her home to school, but it takes her only 10 minutes to walk from school to her home along the same route. What is her average speed, in km/hr, for the round trip?

(A) 3
(B) 3.125
(C) 3.5
(D) 4
(E) 4.5

We can use the formula:

average rate = total distance/total time

Total distance = 2 km

Notice that 30 min = ½ hr and 10 min = ⅙ hr. Therefore, her total time is 1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3 hours.

Thus:

average rate = 2/(2/3) = 6/2 = 3 km/hr

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Re: It takes Mary 30 minutes to walk uphill 1 km from her home to school,   [#permalink] 21 Mar 2019, 18:05
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