A motor-cyclist and a motorist are travelling along two roads which intersect at right angles. The motorist is travelling at 40 km/hour and the motor cyclist is travelling at 60 km/ hour. At a certain instant, the motorist is 30 km due west of the cross roads and the motor-cyclist is 35 km due south of the cross roads, and they are both moving towards the cross roads. Find the time elapsed when the motorist and the motor-cyclist are nearest, verifying that they are then at their nearest.
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