Explanation
Correct answer: D.
Choice D is correct. It is given that is the number of minutes that Adam waits for the bus. The total time it takes Adam to get to school on a day he takes the bus is the sum of the minutes he waits for the bus and the minutes the bus ride takes; thus, this time, in minutes, is . It is also given that the total amount of time it takes Adam to get to school on a day that he walks is minutes. Therefore, gives the values of for which it would be faster for Adam to walk to school.
Desmos solution:
Note: The bus takes w+5 minutes (wait plus 5-minute ride), so walking beats it when w+5 > 20.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect because is not the total length of time for Adam to wait for and then take the bus to school.
Choice B
Choice B is incorrect because is not the total length of time for Adam to wait for and then take the bus to school.
Choice C
Choice C is incorrect because the inequality should be true when walking minutes is faster than the time it takes Adam to wait for and ride the bus, not less.