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To find the average speed of the bike for the whole journey, we can consider the total distance covered and the total time taken.

Let’s assume the total distance covered by the bike is ‘D’. Since the bike travels one-third of the distance at each speed, we can divide the total distance into three equal parts, with each part being (D/3).

Now, let’s calculate the time taken for each one-third distance:

For the first one-third distance: Time = Distance / Speed = (D/3) / 10 = D/30 hours

For the second one-third distance: Time = Distance / Speed = (D/3) / 20 = D/60 hours

For the last one-third distance: Time = Distance / Speed = (D/3) / 60 = D/180 hours

To find the total time taken for the entire journey, we add up the times for each one-third distance:

Total Time = (D/30) + (D/60) + (D/180)

To calculate the average speed, we divide the total distance by the total time:

Average Speed = Total Distance / Total Time = D / [(D/30) + (D/60) + (D/180)]

To simplify the expression, we can find the least common denominator of the fractions in the denominator, which is 180:

Average Speed = D / [(6D + 3D + D) / 180] = D / (10D / 180)

Dividing the numerator and denominator by D:

Average Speed = 180 / 10 = 18 km/hr

Therefore, the average speed of the bike for the whole journey is 18 km/hr.