Problema Solution
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 9 mph and walks back at a speed of 3 mph, how long should she spend walking back?
Answer provided by our tutors
You are solving for the time she will spend walking back, first lets get some formulas down. Let d be the distance of the track, r1 and t1 be her speed and time running, r2 and t2 be he speed walking. Then we have: d = r_{1}t_1{}, d=r_{2}t_{2}, t_1+t_2 = 4
note: since rate is given in mph, t will be measured in hours. Since the distance she will walk and run is the same, setting them equal to each other will give: 7t_1 = 3 t_2, t_1+t_2 = 4
Thus we have a system of equations to solve. t1 = (3/7)t2, so putting that in the second equation: \frac{3}{7}t_2+t_2 = 4 \Rightarrow t_2 = \frac{4}{\frac{10}{7}} = 2.8 hours