A fire covers 420 acres and continues to spread at a rate of 60 acres per day. a.How many total acres will be covered in the next 2 days? b. Then write an expression for the total area covered by the fire in x days. c. The firefighters estimate that they can put out the fire at a rate of 80 acres per day, write an expression for the total area that the firefighters can put out in x days. d. set the expression in parts b and c equal. Solve for x. What does x represent
a. In the next 2 days, the fire will spread at a rate of 60 acres per day. So, the total area covered in the next 2 days would be 60 acres/day x 2 days = 120 acres.
b. Let's assume the original area covered by the fire is A. In x days, the fire will spread at a rate of 60 acres per day. Therefore, the total area covered by the fire in x days can be represented by the expression A + 60x.
c. The firefighters can put out the fire at a rate of 80 acres per day. So, in x days, the total area that the firefighters can put out would be 80 acres/day x x days = 80x acres.
d. Setting the expressions equal:
A + 60x = 80x
To solve for x, we can subtract 60x from both sides:
A = 80x - 60x
A = 20x
So, x represents the number of days it would take for the firefighters to completely put out the fire, considering their rate of extinguishing 80 acres per day.
a. The fire spreads at a rate of 60 acres per day for 2 days, so the total acres covered in the next 2 days would be 60 acres/day * 2 days = 120 acres.
b. The expression for the total area covered by the fire in x days would be: 420 acres + (60 acres/day * x days).
c. The expression for the total area that the firefighters can put out in x days would be: 80 acres/day * x days.
d. Setting the expressions from parts b and c equal, we have:
420 acres + (60 acres/day * x days) = 80 acres/day * x days.
To solve for x, we can first simplify the equation:
420 acres + 60 acres * x = 80 acres * x.
Next, we can move the x terms to one side of the equation:
60 acres * x - 80 acres * x = -420 acres.
Combining like terms gives us:
-20 acres * x = -420 acres.
To isolate x, we can divide both sides of the equation by -20 acres:
x = -420 acres / -20 acres.
Simplifying further:
x = 21.
Therefore, x represents the number of days it would take to cover or put out a certain area in acres.
a. To find the total acres that will be covered in the next 2 days, we need to add the rate at which the fire spreads for 2 days. Since the fire spreads at a rate of 60 acres per day, in 2 days it will cover a total of 2 * 60 = 120 acres.
b. To write an expression for the total area covered by the fire in x days, we can multiply the rate of spread (60 acres per day) by the number of days (x). So the expression is: 60x.
c. To write an expression for the total area that the firefighters can put out in x days, we can multiply the rate at which they can put out the fire (80 acres per day) by the number of days (x). So the expression is: 80x.
d. To set the expressions from parts b and c equal, we have: 60x = 80x.
To solve for x, we can simplify the equation:
60x = 80x
-20x = 0
Dividing both sides by -20, we get:
x = 0
In this case, x represents the number of days it would take for the firefighters to put out the fire completely. However, since x = 0, it means that the rate at which the firefighters can put out the fire is faster than the rate at which it spreads. Therefore, the fire will never be completely put out.
(a) 420 + 2*60 = 540
(b) y = 420 + 60x
(c) z = 80x
(d) 420+60x = 80x
x = 21
The firemen can put out the fire in 21 days.
Check: in 21 days, the fire covers 1680 acres.
in 5 days, the firemen put out 1680 acres