Discussion
With an average speed of 80 km/h, a train reaches its destination on time. If it goes with an average speed of 20 km/h, it is late by 18 minutes. The total journey is.
Answer: D
The journey is 8 km. Let the distance be \(d\) km. The time at 20 km/h exceeds the time at 80 km/h by 18 minutes, which is \(0.3\) h: \[ \frac{d}{20} - \frac{d}{80} = 0.3 \] \[ \frac{4d - d}{80} = 0.3 \] \[ d = \frac{0.3\times 80}{3} = 8 \] Check: 8 km at 80 km/h takes 6 minutes and at 20 km/h takes 24 minutes, a difference of 18 minutes. The values 6, 10 and 18 km do not give that difference.
A shortcut: for one distance at two speeds the time gap is \(d\left(\tfrac{1}{20} - \tfrac{1}{80}\right) = \tfrac{3d}{80}\), and setting it equal to 0.3 hour gives d = 8 km.
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