Answer Key 8.8
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Who or What Rate Time Equation A \(20\) \(t\) \(20t\) B \(25\) \(t\) \(25t\) \(20t+25t=60\)
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Who or What Rate Time Equation A1 \(r\) \(6\) \(6r\) A1 \(r+s\) \(6\) \(6(r+s)\) \(6r+6(r+s)=276\)
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Who or What Rate Time Equation T1 \(25\) \(t\) \(25t\) T2 \(40\) \(t\) \(40t\) \(25t+40t=195\)
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Who or What Rate Time Equation J \(20\) \(5\) \(20(5)\) S \(r\) \(5\) \(r(5)\) \(20(5)+5r=150\)
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Who or What Rate Time Equation P \(r+15\) \(4\) \(4(r+15)\) F \(r\) \(4\) \(4r\) \(4(r+15)+4r=300\)
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Who or What Rate Time Equation A1 \(25\) \(t\) \(25t\) A2 \(35\) \(t\) \(35t\) \(25t+35t=180\)
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Who or What Rate Time Equation Away \(10\) \(t\) \(10(t)\) Return \(3\) \(10-t\) \(3(10-t)\) \(10t=3(10-t)\)
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Who or What Rate Time Equation w \(4\) \(t\) \(4t\) r \(20\) \((3-t)\) \(20(3-t)\) \(4t=20(3-t)\)
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Who or What Rate Time Equation Away \(28\) \(t\) \(28t\) Back \(4\) \(2-t\) \(4(2-t)\) \(\begin{array}{rrlrr}
28t&=&4(2&-&t) \\
28t&=&8&-&4t \\
+4t&&&+&4t \\
\midrule
\dfrac{32t}{32}&=&\dfrac{8}{32}&& \\ \\
t&=&\dfrac{1}{4}&& \\ \\
d&=&rt&& \\
d&=&28(\dfrac{1}{4})&& \\
d&=&7\text{ km}&&\end{array}\)
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Who or What Rate Time Equation Leave \(15\) \(t\) \(15t\) Return \(10\) \(5-t\) \(10(5-t)\) \(\begin{array}{rrlrr}
15t&=&10(5&-&t) \\
15t&=&50&-&10t \\
+10t&&&+&10t \\
\midrule
\dfrac{25t}{25}&=&\dfrac{50}{25}&& \\ \\
t&=&2&& \\ \\
d&=&rt&& \\
d&=&15(2)&& \\
d&=&30\text{ km}&&
\end{array}\) -
Who or What Rate Time Equation To resort \(30\) \(t\) \(30t\) Return \(50\) \(8-t\) \(50(8-t)\) \(\begin{array}{rrlrr}
30t&=&50(8&-&t) \\
30t&=&400&-&50t \\
+50t&&&+&50t \\
\midrule
\dfrac{80t}{80}&=&\dfrac{400}{80}&& \\ \\
t&=&5&& \\ \\
d&=&rt&& \\
d&=&30(5)&& \\
d&=&150\text{ km}&&
\end{array}\) -
Who or What Rate Time Equation To airport \(90\) \(t\) \(90t\) Return \(120\) \(7-t\) \(120(7-t)\) \(\begin{array}{rrlrr}
90t&=&120(7&-&t) \\
90t&=&840&-&120t \\
+120t&&&+&120t \\
\midrule
\dfrac{210t}{210}&=&\dfrac{840}{210}&& \\ \\
t&=&4&& \\ \\
d&=&rt&& \\
d&=&90(4)&& \\
d&=&360\text{ km}&&
\end{array}\) -
Who or What Rate Time Equation Sam \(4\) \(t\) \(4t\) Sue \(6\) \(t-2\) \(6(t-2)\) \(\begin{array}{rrrrr}
4t&=&6(t&-&2) \\
4t&=&6t&-&12 \\
-6t&&-6t&& \\
\midrule
\dfrac{-2t}{-2}&=&\dfrac{-12}{-2}&& \\ \\
t&=&6&& \\
t-2&=&4&&
\end{array}\) -
Who or What Rate Time Equation M1 \(5\) \(t\) \(5t\) M2 \(8\) \(t-6\) \(8(t-6)\) \(\begin{array}{rrrrr}
5t&=&8(t&-&6) \\
5t&=&8t&-&48 \\
-8t&&-8t&& \\
\midrule
\dfrac{-3t}{-3}&=&\dfrac{-48}{-3}&& \\ \\
t&=&16&& \\
t-6&=&10&&
\end{array}\) -
Who or What Rate Time Equation MB \(8\) \(t\) \(8t\) CC \(16\) \(t-2\) \(16(t-2)\) \(\begin{array}{rrrrr}
8t&=&16(t&-&2) \\
8t&=&16t&-&32 \\
-16t&&-16t&& \\
\midrule
\dfrac{-8t}{-8}&=&\dfrac{-32}{-8}&& \\ \\
t&=&4&& \\
t-2&=&2&&
\end{array}\) -
Who or What Rate Time Equation R1 \(6\) \(t\) \(6t\) R2 \(8\) \(t-1\) \(8(t-1)\) \(\begin{array}{rrrrr}
6t&=&8(t&-&1) \\
6t&=&8t&-&8 \\
-8t&&-8t&& \\
\midrule
\dfrac{-2t}{-2}&=&\dfrac{-8}{-2}&& \\ \\
t&=&4&& \\
t-1&=&3&&
\end{array}\) -
Who or What Rate Time Equation M1 \(20\) \(t\) \(20t\) M2 \(30\) \(t\) \(30t\) \(\begin{array}{rrrrl}
20t&+&30t&=&300 \\ \\
&&\dfrac{50t}{50}&=&\dfrac{300}{50} \\ \\
&&t&=&6
\end{array}\) -
Who or What Rate Time Equation T1 \(r\) \(4\) \(4r\) T2 \(r+6\) \(4\) \(4(r+6)\) \(\begin{array}{rrrrrrr}
4r&+&4(r&+&6)&=&168 \\
4r&+&4r&+&24&=&168 \\
&&&-&24&&-24 \\
\midrule
&&&&\dfrac{8r}{8}&=&\dfrac{144}{8} \\ \\
&&&&r&=&18 \\
&&&&r+6&=&24
\end{array}\) -
Who or What Rate Time Equation C1 \(r\) \(3\) \(3r\) C2 \(2r\) \(3\) \(3(2r)\) \(\begin{array}{rrrrl}
3r&+&3(2r)&=&72 \\
3r&+&6r&=&72 \\ \\
&&\dfrac{9r}{9}&=&\dfrac{72}{9} \\ \\
&&r&=&8 \\ \\
&&C_1&=&\phantom{0}8\text{ km/h} \\
&&C_2&=&16\text{ km/h}
\end{array}\) -
Who or What Rate Time Equation P1 \(r-25\) \(2\) \(2(r-25)\) P2 \(r\) \(2\) \(2r\) \(\begin{array}{rrrrrrl}
2(r&-&25)&+&2r&=&430 \\
2r&-&50&+&2r&=&430 \\
&+&50&&&&+50 \\
\midrule
&&&&\dfrac{4r}{4}&=&\dfrac{480}{4} \\ \\
&&&&r&=&120 \\ \\
&&&&P_1&=&120-25=95 \\
&&&&P_2&=&120
\end{array}\) -
Who or What Rate Time Equation S1 \(55\) \(t\) \(55t\) S2 \(40\) \(2.5-t\) \(40(2.5-t)\) \(\begin{array}{rrrrrrr}
55t&+&40(2.5&-&t)&=&130 \\
55t&+&100&-&40t&=&130 \\
&-&100&&&&-100 \\
\midrule
&&&&\dfrac{15t}{15}&=&\dfrac{30}{15} \\ \\
&&&&t&=&2
\end{array}\) -
Who or What Rate Time Equation To end \(8\) \(t\) \(8t\) Return \(3\) \(55-t\) \(3(55-t)\) \(\begin{array}{rrlrr}
8t&=&3(55&-&t) \\
8t&=&165&-&3t \\
+3t&&&+&3t \\
\midrule
\dfrac{11t}{11}&=&\dfrac{165}{11}&& \\ \\
t&=&15&& \\ \\
d&=&r\cdot t&& \\
d&=&8(15)&& \\
d&=&120\text{ m}&&
\end{array}\)
