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Datchile Datchile
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11 years ago
Mike is riding bicycle on a road that can be thought of as having four parts of equal length.  On the first fourth, which is level, he pedals at an average rate of 10 kilometers per hour.  On the second fourth, an upward slope, he travels at an average rate of 5 kilometers per hour.  On the third fourth, a downward slope, he goes at an average rate of 30 kilometers per hour.  On the last fourth, which is level again-but with the wind pushing him, he travels at an average rate of 15 kilometers per hour.  What is Mike's average speed over the entire road?
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wrote...
11 years ago
Just imagine the road has four parts equal length, it doesn't matter what this length is.  For simplicities sake, I'll assume each quarter is 30km long (like I said, huge distance but its irrelevant).

First quarter: He travels at 10km/h, so 30km would take him 3 hours.
Second quarter: 5km/h, 30km takes 6 hours.
Third quarter: 30km/h, 30km takes 1 hour.
Final quarter: 15km/h, 30km takes 2 hours.

So from this you can see he travelled (30x4) = 120km, taking him a total of (3 + 6 + 1 + 2) = 12 hours.

So his average speed is 120km in 12 hours, or 10km/h.
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