# Tomatoes Vs Cucumber

### A battle of the plants which one will come out victorious?

## The Challenge

With the tomatoes starting at 10 cm high and growing at a rate of 5 cm a week.

While the cucumbers start at 6 cm high and are growing at a rate of 7 cm a week.

Their questions are:

- At what week do both of these plants have the same height ?

- Who will win?

*For the table below w stands for week, t stands for tomatoes and c stands for cucumber

*For the graph the green is cucumber and the red is tomato

## The Same Height

**What week do both of these plants have the same height? **

Let *w* represent the number of weeks

Let *h* represent the height

*h* = 5*w*+ 10

For cucumber:

Let *w* represent the number of weeks

Let *h* represent the height

*h *= 7*w* +6

To find at what week they both have the same height :

Cucumbers= Tomatoes

7*w* +6 = 5*w*+ 10

7*w* - 5*w*= 10-6

2*w*/2 = 4/2

* w* = 2

At two weeks they have the same height

To find the height:

*h* = 5*w*+ 10

*h* = 5(2) +10

*h*= 10+10

*h* = 20

**At two weeks at the height of 20 cm both of these plants will be the same height.**

## The Importance

The significance of this situation is that different plants grow at different rates. Just because the cucumber plant starts off smaller doesn’t mean it’ll grow slower than tomatoes which start off a bit taller. Although, thats not actually the case tomato plants can start off higher than other plants but if the growing rate of another plant (in this case cucumbers) is higher the other plant at some point will surpass the height of the tomato plant.

The importance of knowing when the two plants are the same height is that if the competition were to end after 2 weeks both of these plants would be the same height. Making Jim Bob's and Bob Jim's competition a tie.

## The Verdict

**Who's will win?**

It will matter at which week they check, but it will most likely be Bob Jim since the cucumber plant after the 2 week point grows at a much faster rate than the tomato plant.

**The final verdict is that for more than 2 weeks of growing time cucumbers grow faster. Therefore, Bob Jim will win. **