In this type of problem, we would want to use a system of linear equations.
First, we need to find our equations. We know that the two boys traveled 275 km in total, and since x and y count the distance traveled (just in different modes of travel), we can write: x + y = 275.
Next, the problem says that they biked 55 km more than they bussed. So, x = y + 55.
Now that we have two equations to solve for two variables, we can lay them out next to each other:
x + y = 275
x = y + 55
We see that we can substitute x in the first equation with y + 55. This gives us
(y + 55) + y = 275
We solve for y and get y = 110 km by bus. But, we want to know how far they traveled by bike. So, since x = y + 55 and y = 110, we can solve for x by doing 110 + 55 = 165 km by bike.
The answer is 165 kilometers.
