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Sagot :
make chart (rate=speed)
distance=time times rate
D=TR
T=D/R
R=D/T
D T R
J 60 x-2 y+10
M 50 x y
xy=50
(x-2)(y+10)=60
solve for x and y
xy=50
divde both sides by x
y=50/x
subsitute
(x-2)(50/x+10)=60
distribute
50x/x-100/x+10x-20=60
50-100/x+10x-20=60
add like terms
10x-100/x+30=60
10x^2/x-100/x+30=60
(10x^2-100)/x+30=60
subtract 60 from both sides
(10x^2-100)/x-30=0
add 30 to both sides
(10x^2-100)/x=30
multiply both sides by x
10x^2-100=30x
subtract 30x from both sides
10x^2-30x-100=0
factor out the 10
(10)(x^2-3x-10)=0
if you have xy=0 then x and/or y=0 so
10≠0 so (x^2-3x-10)=0
factor by finding what 2 numbers multiply to get -10 and add to get -3
the numbers are -5 and 2 so
(x^2-3x-10)=(x-5)(x+2)=0
so x-5=0
x+2=0
x-5=0
add 5 to both sides
x=5
x+2=0
subtract 2 from both sides
x=-2
false since time cannot be negative
x=5
x times y=50
x=5
5 times y=50
divid eby 5
y=10=Maureen's speed
y+10=10+10=20=Jenny's speed
Jenny's speed is 20 miles per hour
Maureen's speed is 10 miles per hour
distance=time times rate
D=TR
T=D/R
R=D/T
D T R
J 60 x-2 y+10
M 50 x y
xy=50
(x-2)(y+10)=60
solve for x and y
xy=50
divde both sides by x
y=50/x
subsitute
(x-2)(50/x+10)=60
distribute
50x/x-100/x+10x-20=60
50-100/x+10x-20=60
add like terms
10x-100/x+30=60
10x^2/x-100/x+30=60
(10x^2-100)/x+30=60
subtract 60 from both sides
(10x^2-100)/x-30=0
add 30 to both sides
(10x^2-100)/x=30
multiply both sides by x
10x^2-100=30x
subtract 30x from both sides
10x^2-30x-100=0
factor out the 10
(10)(x^2-3x-10)=0
if you have xy=0 then x and/or y=0 so
10≠0 so (x^2-3x-10)=0
factor by finding what 2 numbers multiply to get -10 and add to get -3
the numbers are -5 and 2 so
(x^2-3x-10)=(x-5)(x+2)=0
so x-5=0
x+2=0
x-5=0
add 5 to both sides
x=5
x+2=0
subtract 2 from both sides
x=-2
false since time cannot be negative
x=5
x times y=50
x=5
5 times y=50
divid eby 5
y=10=Maureen's speed
y+10=10+10=20=Jenny's speed
Jenny's speed is 20 miles per hour
Maureen's speed is 10 miles per hour
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