Question

During a race on a circular race track, a race car burns fuel at a constant rate. After lap $4$, the race car has $22$ gallons left in its tank. After lap $7$, the race car has $18$ gallons left in its tank. Assuming the race car does not refuel, after which lap will the race car have $6$ gallons left in its tank?

• A. Lap$13$
• B. Lap$15$
• C. Lap$16$
• D. Lap$19$

Answer 1

The correct option is C Lap$16$

We can write a linear equation $y=mx+c$

Where $x=$ lap number and $y=$ amount of fuel left then.

$x_1=4;$ $y_1=22$

$x_2=7;$ $y_2=18$

Use the slop formula $y-y_1=m(x-x_1)$

$y-22=-\frac{4}{3}(x-4)$

$y=-\frac{4}{3}x+\frac{16}{3}+22$

$y=-\frac{4}{3}x+\frac{82}{3}$

After which lap will the race car have 6 gallons in its tank ?

$y=6$

$-\frac{4}{3}x+\frac{82}{3}=6$

Multiply by $3$ in this equation we get

$-4x+82=3\times 6$

$-4x=18-82$

$x=\frac{-64}{-4}$

$x=16$ is lap where will $16$ gallons left.