Thanks Chris,
hi vest4R,
I would do it exactly the same as Chris, just from a rough hand sketch it is easy to see that the answer lies between t=5 and t=6.
I do not know how to solve it algebraically.
I put this question into WolframAlpha and I am very confused by the information given.
The graph is the same as Chris and I produced and from their graph the answer is t = 5.268
https://www.wolframalpha.com/input/?i=0.5sin(pi*t%2F5)%3D0.1sin(pi*t%2F4)
BUT
The answer that they give is
\(t=40n\qquad n\in Z\\ and\\ t=20(2n+1) \qquad n \in Z \)
This makes NO sense to me what so ever!
Maybe another mathematician can explain to me what WolframAlpha is talking about?