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

Algebra ->  Length-and-distance -> 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      Log On


   

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) About Me  (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 = %28y2+-+y1%29%2F%28x2+-+x1%29+, we have
m = %2818+-+22%29%2F%287+-+4%29+ = -4%2F3 is the slope
:
Find the equation using the point/slope formula: y - y1 = m(x - x1)
y - 22 = -4%2F3(x - 4)
y = -4%2F3x + 16%2F3 + 22
y = -4%2F3x + 16%2F3 + 66%2F3
y = -4%2F3x + 82%2F3 is the equation
:
"after which lap will the racecar have 6 gallons left in its tank?}
y = 6
-4%2F3x + 82%2F3 = 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