Donna hass 6 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 to cool down. If she runs at a speed of 10 mph and walks back at a speed of 2 mph, how long should she plan to spend walking back?
To find out how long Donna should plan to spend walking back, we need to determine the distance of the race first.
Since she runs at a speed of 10 mph, and she has 6 hours to spend training, the distance she runs can be calculated by multiplying her running speed (10 mph) by the time she spends running (x): 10x = distance
Similarly, since she walks back at a speed of 2 mph, the distance she walks back can be calculated by multiplying her walking speed (2 mph) by the time she spends walking (6 - x) since the total time spent is 6 hours: 2(6 - x) = distance
According to the problem, the distance she runs is the same as the distance she walks back, so we can set the two equations equal to each other: 10x = 2(6 - x)
Now let's solve for x. Distributing the 2 on the right side gives: 10x = 12 - 2x
Combining like terms: 10x + 2x = 12
Simplifying: 12x = 12
Dividing both sides by 12: x = 1
So, she should plan to spend 1 hour running and (6 - 1) = 5 hours walking back.