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# The area of a square field is 24200 sq m. How long will a lady take to

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Joined: 02 Sep 2009
Posts: 52294
The area of a square field is 24200 sq m. How long will a lady take to  [#permalink]

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14 Mar 2016, 07:55
00:00

Difficulty:

55% (hard)

Question Stats:

74% (02:41) correct 26% (02:41) wrong based on 137 sessions

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The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?

A. 1 minute
B. 2 minutes
C. 2 minutes 32 seconds
D. 2 minutes 40 seconds
E. 3 minutes

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Re: The area of a square field is 24200 sq m. How long will a lady take to  [#permalink]

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14 Mar 2016, 10:44
1
1
Area of a square field = 24200 sq m
Let the side of square = a
a^2 = 24200
=> a = (24200)^(1/2)
Diagonal = (2)^(1/2) * a
= 1.414 * 155
= 220

Speed of lady = 6.6 km / hour
= 6600 m / hour
= 110 m / min
Time taken by lady to cross the field diagonally = 220/110 = 2 min

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Re: The area of a square field is 24200 sq m. How long will a lady take to  [#permalink]

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15 Mar 2016, 09:11
What level question do you think this is?
Senior SC Moderator
Joined: 22 May 2016
Posts: 2347
The area of a square field is 24200 sq m. How long will a lady take to  [#permalink]

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13 Mar 2018, 10:31
Bunuel wrote:
The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?

A. 1 minute
B. 2 minutes
C. 2 minutes 32 seconds
D. 2 minutes 40 seconds
E. 3 minutes

These numbers are a lot easier than they appear to be. Fractions help here.

1) Find the length of the square field's sides and diagonal, D, with factoring.
Look for s=root of a perfect square and, since $$D=s\sqrt{2}$$, look for $$\sqrt{2}$$

$$s^2=A$$
$$s=\sqrt{A}=\sqrt{24,200(m^2)}$$
$$s=\sqrt{(2*12,100)m^2}=\sqrt{(2*110*110)m^2}$$
$$s=110\sqrt{2}m$$

Diagonal length =$$(s\sqrt{2})m$$
$$D=(110\sqrt{2}*\sqrt{2})m=(110*2)m= 220m$$

2) Convert diagonal length from $$m$$ to $$km$$
$$(1,000m=1km)=>(1m=\frac{1}{1000}km)$$
$$D=(220m*\frac{1km}{1000m})=\frac{220}{1000}km=\frac{11}{50}km$$

3) Convert rate to a fraction
$$6.6kmh=6\frac{3}{5}=\frac{33}{5}kmh$$

4) Find time. $$R*T=D$$, and $$T=\frac{D}{R}$$
$$T=\frac{\frac{11}{50}km}{\frac{33}{5}kmh}=(\frac{11}{50}km*\frac{5}{33}kmh)=\frac{1}{30}hour$$

Any fraction of an hour * 60 = # of minutes

$$T= \frac{1}{30}hr*60\frac{min}{hr}=2$$
minutes

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Re: The area of a square field is 24200 sq m. How long will a lady take to  [#permalink]

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14 Mar 2018, 15:05
Bunuel wrote:
The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?

A. 1 minute
B. 2 minutes
C. 2 minutes 32 seconds
D. 2 minutes 40 seconds
E. 3 minutes

Recall that the diagonal, d, of a square, in relation to its area, A, is given by the formula: A = d^2/2. Thus we have:

24,200 = d^2/2

48,400 = d^2

d = √48,400 = 220 m

Now we can set up a proportion to find the time, t, it takes to walk along the diagonal of the square (recall that 6.6 km = 6,600 m and 1 hr = 60 min):

220/t = 6,600/60

220/t = 110

t = 220/110 = 2 min

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Re: The area of a square field is 24200 sq m. How long will a lady take to &nbs [#permalink] 14 Mar 2018, 15:05
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# The area of a square field is 24200 sq m. How long will a lady take to

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