Question is in description.

Question

April has 5 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 8 mph and walks back at a speed of 2 mph, how long should she plan to spend walking back?

Answer 1

distance=rate*time

d=rt

d=8t

d=2(5-t)

8t=2(5-t)

8t=10-2t

8t+2t=10

10t=10

t=1

5-1=4 hours walking back

Answer 2

Hi Shatoria, we can use the D(istance) = R(ate) * T(ime) formula to find the answer to your question.

 

We know the distance April ran and walked is the same. We know the total time April has to train is 5 hours. Using the D = R * T formula, we can find D. Using D, we can find the time April will need to walk back to the starting point.

 

Training Run:

 

D = R_t * T_t

 

D = 8 * T_t

 

T_t = D / 8

 

Walking Back:

 

D = R_w * T_w 

 

D = 2 * T_w

 

T_w = D / 2

 

Total time:

 

We know the total time is 5 hours, therefore, T_t + T_w must equal 5.

 

T_t + T_w = 5

 

Substitute for T_t and T_w:

 

D / 8 + D / 2 = 5

 

Solve for D by multiplying all terms by 8 (this clears the fractions):

 

D + 4D = 40

 

5D = 40

 

Divide both sides by 8:

 

D = 8

 

We know the distance April ran and walked is 8 miles.

 

Now, return to the walking back equation to find the time she walked back to the starting point.

 

D = R_w * T_w

 

Substitute for D and R_w:

 

8 = 2 * T_w

 

Divide both sides by 2:

 

T_w = 4

 

April needs 4 hours to return to her starting point.

 

Questions?