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Dana has 4 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 run at a speed of 8 mph and walks back at a speed of 2 mph, how long should she plan to spend walking back

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opudodennis

Answer:

2hrs 40 minutes

Step-by-step explanation:

The formula for distance is expressed as:

[tex]d=st, s=speed, t=time[/tex]

#The time taken to run:

[tex]d=st\\\\t=d/s\\\\t_r=d/8[/tex]

#The time taken to walk:

[tex]d=st\\\\t=d/s\\\\t_w=d/2[/tex]

#Since the distances are the same:

[tex]d_r=8t_r,d_w=2t_w\\\\8t_r=2t_w\\\\t_r+t_w=4->t_w=4-t_r\\\\\therefore8t_r=2(4-t_r)\\\\8t_r=8-2t_r\\\\t_r=1\frac{1}{3} \hrs\\\\t_w=4-1\frac{1}{3}=2\frac{2}{3}\ hrs[/tex]

Hence, Dana spends 2hrs 40 minutes walking back

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