a. It spends 2.04 hours going 55 mph.
b. It will spend 1 hour going 35 mph.
c. The trip will take 3.64 hours.
Step-by-step explanation:
Given equation is;
55x + 35y = 200
Where
x represent the time when speed is 55 mph
y represent the time when speed is 35 mph
a. If the car spends 2.5 hours going 35mph on the trip, how long does it spend going 55mph?
Putting y=2.5 in given equation
[tex]55x+35(2.5)=200\\55x+87.5=200\\55x=200-87.5\\55x=112.5\\[/tex]
Dividing both sides by 55
[tex]\frac{55x}{55}=\frac{112.5}{55}\\x=2.04\ hours[/tex]
It spends 2.04 hours going 55 mph.
b. If the car spends 3 hours going 55mph on the trip, how long does it spend going 35mph?
Putting x=3 in given equation
[tex]55(3)+35y=200\\165+35y=200\\35y=200-165\\35y=35[/tex]
Dividing both sides by 35
[tex]\frac{35y}{35}=\frac{35}{35}\\y=1[/tex]
It will spend 1 hour going 35 mph.
c. If the car spends no time going 35mph, how long would the trip take?
Putting y=0 in given equation
[tex]55x+35(0) = 200 \\55x+0=200\\55x=200[/tex]
Dividing both sides by 55
[tex]\frac{55x}{55}=\frac{200}{55}\\x=3.636[/tex]
Rounding off
x = 3.64
The trip will take 3.64 hours
Keywords: linear equation, division
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