Hello, defeated_soldier!
A strange problem
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The winning relay team in a high school sports competition clocked 48 min for a distance of 13.2 km.
The runners A, B, C and D maintained speeds of 15 kph,16 kph, 17 kph and 18kph, respectively.
What is the ratio of the time taken by B to the time taken by D ?
\(\displaystyle a)\;5:16\;\;\;\;b)\;5:17\;\;\;\;c)\;9:8\;\;\;\;d)\;8:9\)
In a relay race, each runner runs the same distance . . . call it \(\displaystyle d.\)
Runner \(\displaystyle B\) ran \(\displaystyle d\) km at 16 kph . . . His time: \(\displaystyle \,t_{_B}\,=\,\frac{d}{16}\) hours.
Runner \(\displaystyle D\) ran \(\displaystyle d\)km at 18 kph . . . His time: \(\displaystyle \,t_{_D}\,=\,\frac{d}{18}\) hours.
The ratio of their times is: \(\displaystyle \L\,\frac{t_{_B}}{t_{_D}}\;=\;\frac{\frac{d}{16}}{\frac{d}{18}}\;=\;\frac{18}{16}\;=\;\frac{9}{8}\)
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Neither the total time nor the length of the track was relevant.
In fact, the "48 minutes" is very sloppy time-keeping.
Each runner ran 3.3 km at his respective speed.
The total time is: \(\displaystyle \,\frac{3.3}{15}\,+\,\frac{3.3}{16}\,+\,\frac{3.3}{17}{\,+\,\frac{3.3}{18} \:=\:\frac{9837.3}{12240}\:=\:0.80370098\) hours
\(\displaystyle \;\;\)which equals 48 minutes, 13.32 seconds.
And track events are measured to the nearest hundredth of a second.
