Final answer:
The ratio of Matt's home-to-work time to work-to-home time is 2:1. This means that the outgoing journey takes twice as long as the return journey. Option number b is correct.
Step-by-step explanation:
If it takes Matt twice the time to drive from home to work compared to his return journey, we are looking for the ratio of his home-to-work time to work-to-home time. To find this ratio, let's denote the time it takes for Matt to travel from work to home as t. Accordingly, the time it takes for him to go from home to work would be 2t, as it is stated to be twice as long.
The ratio of the time spent on the home-to-work journey to the work-to-home journey is therefore 2t/t. When we calculate this, we simply divide 2t by t, which gives us 2. This means that the ratio of the home-to-work time to the work-to-home time is 2:1, corresponding to answer choice (b) 2:1.
This ratio indicates that for every unit of time Matt spends on the return journey, he spends two units of time on the outgoing journey, which seems reasonable considering the problem has explicitly described the outgoing journey to take twice as long. We ensure the answer is reasonable by relating it to the given problem context.