Answer Key 8.8

Who or What Rate Time Equation

A $20$ $t$ $20t$

B $25$ $t$ $25t$

$20t+25t=60$
Who or What Rate Time Equation

A₁ $r$ $6$ $6r$

A₁ $r+s$ $6$ $6(r+s)$

$6r+6(r+s)=276$
Who or What Rate Time Equation

T₁ $25$ $t$ $25t$

T₂ $40$ $t$ $40t$

$25t+40t=195$
Who or What Rate Time Equation

J $20$ $5$ $20(5)$

S $r$ $5$ $r(5)$

$20(5)+5r=150$
Who or What Rate Time Equation

P $r+15$ $4$ $4(r+15)$

F $r$ $4$ $4r$

$4(r+15)+4r=300$
Who or What Rate Time Equation

A₁ $25$ $t$ $25t$

A₂ $35$ $t$ $35t$

$25t+35t=180$
Who or What Rate Time Equation

Away $10$ $t$ $10(t)$

Return $3$ $10-t$ $3(10-t)$

$10t=3(10-t)$
Who or What Rate Time Equation

w $4$ $t$ $4t$

r $20$ $(3-t)$ $20(3-t)$

$4t=20(3-t)$
Who or What Rate Time Equation

Away $28$ $t$ $28t$

Back $4$ $2-t$ $4(2-t)$

$\begin{array}{rrlrr} 28t&=&4(2&-&t) \\ 28t&=&8&-&4t \\ +4t&&&+&4t \\ \midrule \dfrac{32t}{32}&=&\dfrac{8}{32}&& \\ \\ t&=&\dfrac{1}{4}&& \\ \\ d&=&rt&& \\ d&=&28(\dfrac{1}{4})&& \\ d&=&7\text{ km}&& \end{array}$
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 $3$ $55-t$ $3(55-t)$

$\begin{array}{rrlrr} 8t&=&3(55&-&t) \\ 8t&=&165&-&3t \\ +3t&&&+&3t \\ \midrule \dfrac{11t}{11}&=&\dfrac{165}{11}&& \\ \\ t&=&15&& \\ \\ d&=&r\cdot t&& \\ d&=&8(15)&& \\ d&=&120\text{ m}&& \end{array}$

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