27) 5 hours

Distance covered forward journey = Distance covered reverse journey = 20 ÷ 2 = 10 km

Let distance covered on flat  = F
Let time taken to cover flat surface = f
Speed on flat = 4
F = 4 x f = 4f

Let distance covered uphill  = U
Let time taken to cover uphill surface = u
Speed on uphill = 3
U = 3 x u= 3u

Let distance covered downhill  = D
Let time taken to cover downhill surface = d
Speed on downhill = 6 (which is twice the speed on uphill)
D = 6 x d= 6d = 10 km

We know that the distance covered uphill = distance covered down hill

Hence, we get the equation:

U = D
3u = 6d
u = 2d

Forward journey + reverse journey = 20km

4f + 3u + 4f + 6d = 20
4f + 6d + 4f + 6d = 20
8f + 12d = 20
4(2f + 3d) = 20
2f + 3d = 5

Hence the answer is 5 hours.

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