Answer:
140 minutes
Step-by-step explanation:
Using m = (y₂ - y₁)/(x₂ - x₁) , we find the rate at which Snail A moves which is also the gradient of the line with which it moves. Given that Snail A was 12.5 inches above the ground at 10 minutes and 16 inches above the ground at 24 minutes, x₁ = 10 min, y₁ = 12.5 inches, x₂ = 24 min and y₂ = 16 inches.
So, m = (y₂ - y₁)/(x₂ - x₁)
m = (16 - 12.5)/(24 - 10) = 3.5/14 = 0.25
Also, the equation of the line,
(y - y₁)/(x - x₁) = m
(y - 12.5)/(x - 10) = 0.25
cross-multiplying, we have
y - 12.5 = 0.25(x - 10)
expanding the bracket, we have
y - 12.5 = 0.25x - 2.5
adding 12.5 to both sides, we have
y - 12.5 + 12.5 = 0.25x - 2.5 + 12.5
y = 0.25x + 10
Since Snail B started at 3 inches above the ground and climbed 0.3 inch per minute. The snails continued at the same speeds, its distance y moved is y = 0.3t + 3
We now find the time x it takes the snails to cover the same distance by equating both expressions. So,
0.25x + 10 = 0.3x + 3
collecting like terms, we have
10 - 3 = 0.3x - 0.25x
7 = 0.05x
0.05x = 7
x = 7/0.05
x = 140 minutes
