Janelle has 66 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 7mph7⁢mph and walks back at a speed of 3mph3⁢mph, how long should she plan to spend walking back?

To solve this problem, we first need to understand that the total time Janelle has for training is divided into two parts: the time she spends running and the time she spends walking back.

1. Let's denote the distance of the race as D (in miles). We know that the speed is distance divided by time, so the time spent running can be calculated as D/7 (in hours).

2. Similarly, the time spent walking back is D/3 (in hours).

3. The total time spent training is the sum of the time spent running and the time spent walking back, which is D/7 + D/3.

4. We know that the total time spent training is 66 hours, so we can set up the equation D/7 + D/3 = 66.

5. To solve this equation for D, we first need to find a common denominator for the fractions, which is 21. So the equation becomes 3D/21 + 7D/21 = 66.

6. Simplifying this gives us 10D/21 = 66.

7. Solving for D, we get D = 66 * 21 / 10 = 138.6 miles.

8. Now that we know the distance of the race, we can calculate the time spent walking back, which is D/3 = 138.6 / 3 = 46.2 hours.

So, Janelle should plan to spend approximately 46.2 hours walking back.