What is the simplest radical form of the expression? (8x^5y^3)^(2/3)
1 answer:
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Answer:
k = 5
Step-by-step explanation:
Suppose the distance to the factory is 1 unit. Then the speed the father walks is ...
speed = distance/time = 1 / 30 . . . . units per minute
When the father leaves 10 minutes earlier than the son, his position t minutes after the son starts walking is ...
d = 1/30(t +10)
Similarly, when the father starts 5 minutes earlier than the son, his position t minutes after the son starts walking is ...
d = (1/30)(t +5)
We want that to be the same as the distance the son covers t minutes after he starts walking. The son's progress is ...
d = 1/20t
To find the value of k such that the distance covered is the same 2k minutes after the son starts, we will use t=2k and d=d, so ...
(1/30)(2k +5) = (1/20)(2k)
4k +10 = 6k . . . . . multiply by 60
10 = 2k . . . . . . . . . subtract 4k
5 = k . . . . . . . . . . . divide by 2
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The attached graph shows the different scenarios, where the blue line is the son's progress. When the father starts 5 minutes earlier, the son meets him half-way to the factory after 10 minutes, so k = 10/2 = 5.
