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# help

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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?

Jun 10, 2020

#1
+25541
+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.

Jun 10, 2020
#2
+26620
+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

Jun 10, 2020