after how many days of growth will plant B be twice as tall as plant A?

Question

Plant A is planted at 7cm tall and grows 1.5 per day.

Plant B is planted at 2cm tall and grows 4.2cm per day

Answer 1

On any given day (d) after being planted, the height of plant A will be h(A) = 7 + 1.5*d cm

On any given day (d) after being planted, the height of plant B will be h(B) = 2+ 4.2*d cm

We want to know when h(B) = 2*h(A)  or

2 + 4.2*d = 2*[7 + 1.5*d]

Solving for d:

4.2*d = 2*[7 + 1.5*d] - 2 = 14 + 3*d - 2 = 12 + 3*d

subtracting 3*d from both sides results in:

1.2*d = 12

dividing both sides by 1.2 yields the answer: d = 10

 

Check: On day 10, Plant A is 7 + 1.5*10 + 7 + 15 = 22 cm tall

Plant B is 2 + 4.2*10 = 2 + 42 = 44 cm tall

44 = 2* 22

QED