Question

the mens world record (as of 2007) for swimming 1500 m in a long course pool is 14 min 34.56 s. at this rate, how many seconds would it take the mens world record holder to swim 0.150 mi? (1 mi = 1609 m)
time: 18400
incorrect answer
enter numeric value

Explanation:

Step1: Convert total time to seconds

First, convert 14 minutes to seconds. Since 1 minute = 60 seconds, 14 minutes is \(14\times60 = 840\) seconds. Then add the remaining 34.56 seconds. So total time \(t_{total}=840 + 34.56=874.56\) seconds.

Step2: Find the speed in m/s

The distance for the record is 1500 m. Speed \(v=\frac{\text{distance}}{\text{time}}=\frac{1500\space m}{874.56\space s}\approx1.715\space m/s\) (we can keep more precision for now).

Step3: Convert 0.150 mi to meters

Given 1 mi = 1609 m, so 0.150 mi is \(0.150\times1609 = 241.35\) m.

Step4: Calculate time for 0.150 mi

Using \(t=\frac{d}{v}\), where \(d = 241.35\) m and \(v=\frac{1500}{874.56}\) m/s. So \(t=\frac{241.35}{\frac{1500}{874.56}}=241.35\times\frac{874.56}{1500}\).

First, calculate \(241.35\times874.56 = 241.35\times800 + 241.35\times74.56=193080+241.35\times74.56\). \(241.35\times74.56\approx241.35\times70 = 16894.5\), \(241.35\times4.56\approx1100.556\), so total \(\approx16894.5 + 1100.556 = 17995.056\). Then \(17995.056+193080 = 211075.056\). Then divide by 1500: \(\frac{211075.056}{1500}\approx140.7167\) seconds.

Alternatively, we can do it using proportion:

Let \(t\) be the time for 0.150 mi.

\(\frac{1500\space m}{874.56\space s}=\frac{0.150\times1609\space m}{t}\)

Cross - multiply: \(1500t=874.56\times(0.150\times1609)\)

\(1500t = 874.56\times241.35\)

\(1500t=874.56\times241.35\)

Calculate \(874.56\times241.35\):

\(874.56\times241.35=(800 + 74.56)\times241.35=800\times241.35+74.56\times241.35\)

\(800\times241.35 = 193080\)

\(74.56\times241.35\approx74.56\times200+74.56\times41.35 = 14912+3083.056 = 17995.056\)

So \(874.56\times241.35=193080 + 17995.056=211075.056\)

Then \(t=\frac{211075.056}{1500}\approx140.72\) seconds (rounded to two decimal places)

Answer:

\(141\) (or more precisely \(140.72\))