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I hope you can use variables, "x"'s.
Denote the length of the tour to Japan as J days, to Hong Kong as H and to Europe as E. What is given about them?
"the tour of Japan is twice as long as the tour of Hong Kong" may be written as
J = 2*H.
"the tour of Japan is half as long as the tour of Europe" means
J = E/2, or the same may be written as E = 2*J.
And "the three tours last eight weeks altogether" means
J + H + E = 8*7 = 56 (days, because a week has 7 days).
Now go for solution.
If E = 2*J and J = 2*H, then E = 2*(2*H) = 4*H.
Now substitute J = 2*H and E = 4*H into the third equation:
2*H + H + 4*H = 8*7.
The left side is equal to 7*H as 2+1+4=7, and 7*H = 8*7 easily gives that H=8 (days).
Now recall that J = 2*H = 2*8 = 16 (days). This is the answer.
(we can also find E=4*H=4*8=32 days)
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