Terry, a marathon runner ran from her house to the high school then back. The return trip took 5 minutes longer. If her speed was 10 mph to the high school and 9 mph to her house, How far is Terry's house from the high school?

Guest Jun 10, 2020

#1**+1 **

**Terry, a marathon runner ran from her house to the high school then back. **

**The return trip took 5 minutes longer. If her speed was 10 mph to the high school and 9 mph to her house, **

**How far is Terry's house from the high school?**

\(\begin{array}{|rcl|c|rcl|} \hline &(1)& && &(2) \\ \hline \mathbf{v_1} &=& \mathbf{\dfrac{s}{t}} && \mathbf{v_2} &=& \mathbf{\dfrac{s}{t+\dfrac{5}{60} }} \\ && & \boxed{v_1 = 10,\ v_2 = 9 }\\ 10 &=& \dfrac{s}{t} && 9 &=& \dfrac{s}{t+\dfrac{5}{60} } \\\\ \mathbf{t} &=& \mathbf{\dfrac{s}{10}} && 9 &=& \dfrac{s}{t+\dfrac{5}{60} } \\\\ & & && 9\Big(t+\dfrac{5}{60}\Big) &=& s \\\\ & & && 9t+\dfrac{9*5}{60} &=& s \\\\ & & && 9t+0.75 &=& s & \mathbf{t=\dfrac{s}{10}} \\\\ & & && \dfrac{9s}{10}+0.75 &=& s & | \quad * 10 \\\\ & & && 9s + 7.5 &=& 10s \\ & & && \mathbf{s} &=& \mathbf{7.5} \\ \hline \end{array}\)

Terry's house from the high school is **7.5 miles** far away.

heureka Jun 10, 2020

#2**+1 **

d = distance the same both ways

rate * time = d

10 m/hr *x = 9 m/hr * (x + 1/12 ) 5 min = 1/12 hr

10x = 9x + 9/12

x = 9/12 hr

in 9/12 hr at 10m/hr Terry covers the distance of 7.5 miles

ElectricPavlov Jun 10, 2020