Question

you swim 3.6 kilometers per hour. how long (in minutes) will it take you to swim the distance d across the pond?

Explanation:

Step1: Prove the similarity of triangles

Since \(\angle ABC=\angle DEC = 90^{\circ}\) and \(\angle ACB=\angle DCE\) (vertical angles are equal), by the AA (Angle - Angle) similarity criterion, \(\triangle ABC\sim\triangle DEC\).

Step2: Use the property of similar triangles

For similar triangles \(\triangle ABC\) and \(\triangle DEC\), we have the proportion \(\frac{AB}{DE}=\frac{BC}{EC}\). Substituting \(AB = 105m\), \(BC=140m\), and \(EC = 80m\), we get \(\frac{105}{d}=\frac{140}{80}\). Cross - multiplying gives \(140d=105\times80\), so \(d=\frac{105\times80}{140}=60m\).

Step3: Convert the speed unit

The speed \(v = 3.6\) kilometers per hour. Convert it to meters per minute. Since \(1\) kilometer \(= 1000\) meters and \(1\) hour \(= 60\) minutes, \(v=\frac{3.6\times1000}{60}=60m/min\).

Step4: Calculate the time

Using the formula \(t=\frac{s}{v}\) (where \(s\) is distance and \(v\) is speed), with \(s = d=60m\) and \(v = 60m/min\), we have \(t=\frac{60}{60}=1\) minute.

Answer:

\(1\) minute