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
Answer B
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