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A father and his son go out for a 'walk-and-run' every morning around a track formed by an equilateral triangle. The father's walking speed is 2 mph and his running speed is 5 mph. The son's walking and running speeds are twice that of his father. Both start together from one apex of the triangle, the son going clockwise and the father anti-clockwise. Initially the father runs and the son walks for a certain period of time. Thereafter, as soon as the father starts walking, the son starts running. Both complete the course in 45 minutes. For how long does the father run? Where do the two cross each other?

Read Solution (Total 1)

Let the perimeter of the equilateral triangle = x
Let xf1,xf2,xs1 and xs2 be the distance covered by father and son in Act 1 and Act 2 resp. (The definition of Act is given below)
So, x= xf1+xf2 = xs1+xs2
First Act: Son walks and Father runs for time = t1
Second Act: Son runs and Father walks for time = t2
t = t1 + t2
So, 45 = xf1/5 + xf2/2 = xs1/4 + xs2/10
But xf1/5 = xs1/4 and xf2/2 = xs2/10

Solving, we get,
xf1 = 200
xf2=10
xs1=160
xs2=50
13 years agoHelpfull: Yes(1) No(3)

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