I have a trekking bike. Should I buy a road bike to train for a race? I have a trekking bike (similar to this one : http://www.hervis.at/products/product?code=BASE:1842986&amp;referer=at-bike-cross )  and I plan to join some triathlon events in the future. I try to do some long runs (sorry if that is not that long for you) around 70-80 km, but I cannot be faster than 21 km/h. I see the others with road bikes are much quicker than me(but I don't know whether this is because of me or the bike). 

My first point is that I dont want to spend money now and I am really undecided whether this is a good strategy to train for later. Do you think there is room for big speed improvement with the road bikes? Is it similar to train with the trekking bike and then change it or does it change the style a lot?
Yes, you will need to have a road bike in order to properly train for a Triathlon. The ergonomics of a road bike a totally different to a mountain bike and you will therefore have to set aside some extra time for your body. You may at first feel discomfort when riding as you won't be used to the bike, but that'll go away very quickly.

As to whether you should buy a bike right now or not: I would say wait until autumn time when bicycle retailers will be cutting their prices in order to get rid of the current season bikes. I got my bike for £240 and it was Originally £600.