Runner A completes 51/3 laps around a track in the same amount of time it takes Runner B to complete 6 laps. B's pace is 7.5 minutes per mile. How many seconds longer will it take Runner A to run 1 mile compared to B.
6 laps / 5 1/3 laps =12.5% is runner B faster than runner A.
If runner B run a mile in 7.5 minutes, then:
7.5 x 1.125 =8.4375 - minutes for runner A to run a mile.
8.4375 - 7.5 =0.9375 - minutes longer that takes runner A to run a mile.
0.9375 x 60 =56.25 seconds longer for runner A to run the same mile.
+773 Runner A's speed in laps, 17 laps per x.
Runner B's speed in laps, 6 lags per x.
The ratio is \(\dfrac{7.5}{z} = \dfrac{17}{6}\). Cross multiplying, we have \(17z = 45 \Rightarrow z = 2.647 \). 2.647 minutes is roughly 159 seconds. 7.5 minutes is 450 seconds.
450 - 159 = \(\boxed{291}\) seconds.
- PM
+773 Realize that the ratio is inverse.
The MORE laps in time, the better.
The LESS time for a mile, the better.
MORE does not equal LESS, so we need to get the reciprocal of LESS to have \(MORE = \dfrac{1}{LESS}\).
6 laps / 5 1/3 laps =12.5% is runner B faster than runner A.
If runner B run a mile in 7.5 minutes, then:
7.5 x 1.125 =8.4375 - minutes for runner A to run a mile.
8.4375 - 7.5 =0.9375 - minutes longer that takes runner A to run a mile.
0.9375 x 60 =56.25 seconds longer for runner A to run the same mile.
