in eleven hours c walks 12.5km less than d  in 12 hours and in five hours. d walks 13\4km less than c does in seven hours. how many km does each walk per hour?

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tjbrewer | Elementary School Teacher | (Level 2) Associate Educator

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If we use c and d to designate their respective rates of speed, we can express the relationships in the question mathematically

`11c=12d-12.5` and `5d=7c-13/4`

We can find their respective rates of speed by solving one of the equations for one variable, inserting that value into the other equation, and then substitute the variable value found into the first equation to find the other variable's value. 

`11c=12d-12.5->c=12/11 d-12.5/11` we substitute into the other equation and it becomes `5d=7(12/11 d-12.5/11)-13/4` we simplify and get `5d=84/11 d-87.5/11-13/4` combine like terms `5d=84/11 d-493/44` subtract `84/11 d` from each side and we get `-29/11 d=-493/44`` ` Divide each side by -29/11 and `d=4.25` km/h

Then we substitute that value for d back into the equation solved for c and we find `c=12/11 xx 4.25-12.5/11=3.5`` ` km/h

c and d walk 3.5 km/h and 4.25 km/h respectively. 

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