Word Problem Question, Please help

Question

Dana has 3 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 8mph and walks back at a speed of 2
mph, how long should she plan to spend walking back?

Answer 1

Although we don't know the time spent running (R) or walking (W), we know they add up to 3 hours

R + W = 3    Eqn. 1

 

D = rt

We can also write expressions for the distance running:

D = 8R

and walking:

D = 2W

The distance is the same in both directions, D = D, so:

8R = 2W    Eqn. 2

 

We need to find W, so solve equation 1 for R in terms of W:

R = 3-W

 

Substitute this for R in equation 2:

8(3-W) = 2W

24-8W = 2W

24 = 2W + 8W = 10W

W = 2.4 hours = 2 hours 24 minutes

 

Check:

R = 3-W = 3-2.4 = 0.6

D = 8R = 2W

(8)(0.6) = (2)(2.4)

4.8 = 4.8

(And the distance is 4.8 miles)