Most efficient way to solve these equations ?

Let's look at the actual question (two part analysis - question 1)

Work crews Alpha and Zeta are repaving a section of freeway in Los Angeles. Work crew Alpha started its work one week (40 working hours) earlier than work crew Zeta, and started on the north end of the freeway, working its way south at a rate of 12 meters per hour since starting the job. Now, work crew Zeta has started at the south end, working its way north at a rate of 10 meters per hour. The section of freeway that needs to be repaved is 1.5 kilometers long, including the section that has already been paved.

Given that each crew will not necessarily work the same number of hours, which of the following answer choices represents an hourly workload for each crew that will finish the project?
Number of Hours
10
20
30
40
50
60

Solution:

Let's try to find the leftover work.
1500 - 40*12 = 1020 m

12a + 10b = 1020

You have to find the values that fit for a (Alpha) and b (Zeta)
You see that it is easy to put in a value for 'b' and subtract that from 1020.

Say b = 10, 12a = 920 (but 92 is not divisible by 12 so not possible)
Say b = 20, 12a = 820 (but 82 is not divisible by 12 so not possible)
Say b = 30, 12a = 720
a must be 60 because 12*60 = 720