# if the tour of japan is twice as long as the tour of hong kong but half as long as the tour of Europe. if the three tours last eight weeks altogether, how long is the tour of japan?

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Borys Shumyatskiy | Certified Educator

Hello!

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)