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In most problems, it is assumed that you know information implied by the context of the problem, but not stated outright. Unless otherwise stated, you should assume the following:
- There is zero friction, unless you are given friction information;
- Velocities are constant, unless forces or accelerations are known; and
- Initial position, time, and velocity are zero, unless you know otherwise.
Try to relate all the information you are given to the variables you chose. If you are stumped, think about what additional assumptions you might make that would make a problem solvable. 
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The two bicycles are 500 m apart at the start, which is t = 0. To use this information, we need to relate it to the distance variables we defined. By the time they meet, the total distance traveled by both bicycles together has to be 500 m. In problem-specific variables this is written as d1 + d2 = 500 m. This is a third equation. Now we need a fourth equation because there are four unknowns.
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The last equation comes from reading the problem and recognizing that the bicyclists meet after traveling the same amount of time. Mathematically, that means t1 = t2 = t. Since the times are equal, they do not need subscripts for us to tell them apart. We can write the three equations in terms of a single time t.
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We now know enough to solve the problem.
Sentences from the problem and their mathematical equivalents are shown above.
One unknown distance equation is d1 = v1t. The other unknown distance equation is d2 = v2t. This is true no matter what value t has. The distance relationship tells you that d1 + d2 = 500 m. You can now replace the distances with their equivalent velocities and times. This gives you a single equation with a single unknown value. That unknown value is what you want because then you can calculate an answer.
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