# Rick goes cycling every morning. He starts in a straight line and cycles 3 km in 24 minutes. Then takes a left and cycles 2 km in 6 minutes. Then takes a left again and cycles at x km/h for 12 min....

Rick goes cycling every morning. He starts in a straight line and cycles 3 km in 24 minutes. Then takes a left and cycles 2 km in 6 minutes. Then takes a left again and cycles at x km/h for 12 min. If Rick's velocity is 2 km/h, what is the value of x.

justaguide | College Teacher | (Level 2) Distinguished Educator

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Rick goes cycling every morning. He starts cycling in a straight line and rides for 3 km in 24 minutes. Then he takes a left and rides 2 km in 6 minutes. He takes a left again and cycles at x km/h for 12 min.

The velocity of Rick in doing this is equal to 2 km/h. To find the value of x, first the displacement of Rick has to be determined.

The magnitude of his displacement in the initial direction he rides in is equal to 3 - x*(12/60). The displacement in the perpendicular direction is 2 km. This gives the displacement from the point he starts from as `sqrt((3 - x*(12/60))^2 + 2^2)` . The total time taken by Rick is `(24+6)/60 + (12/60) = 7/10`

`sqrt((3 - x*(12/60))^2 + 2^2)/(7/10) = 2`

=> `sqrt((3 - x*(12/60))^2 + 2^2) = 14/10`

=> `(3 - x*(12/60))^2 + 2^2) = 1.4^2`

=> `(3 - x*(12/60))^2 = -51/25`

But the square of a real number cannot be negative.

There is no value for x that satisfies the values given in the problem.