SOLUTION: During a race on a circular track, a racecar burns fuel at a constant rate. After lap 4, the racecar has 22 gallons left in its tank. After lap 7, the racecar has 18 gallons left i

Question 1074235: During a race on a circular track, a racecar burns fuel at a constant rate. After lap 4, the racecar has 22 gallons left in its tank. After lap 7, the racecar has 18 gallons left in its tank. Assuming the racecar does not refuel, after which lap will the racecar have 6 gallons left in its tank?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
During a race on a circular track, a racecar burns fuel at a constant rate.
After lap 4, the racecar has 22 gallons left in its tank. After lap 7, the racecar has 18 gallons left in its tank.
Assuming the racecar does not refuel, after which lap will the racecar have 6 gallons left in its tank?
:
We can write a linear equation y = mx + b
where x = lap number and y = amt of fuel left
then
x1 = 4; y1 = 22
x2 = 7; y2 = 18
use the slope formula: m = , we have
m = = is the slope
:
Find the equation using the point/slope formula: y - y1 = m(x - x1)
y - 22 = (x - 4)
y = x + + 22
y = x + +
y = x + is the equation
:
"after which lap will the racecar have 6 gallons left in its tank?}
y = 6
x + = 6
multiply equation by 3 to get rid of the denominators
-4x + 82 = 3(6)
-4x = 18 - 82
-4x = -64
x = -64/-4
x = 16 is lap where he will 6 gal left

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