Question

Water is leaking out of two containers.

The water started to leak out of the containers at the same time.
The straight line P shows information about the amount of water, in litres, in container P.
The straight line Q shows information about the amount of water, in litres in container Q.
(a) Work out the gradient of line P
One container will become empty first
(b) (i) Which container?
You must explain your answer
(ii) How much water is then left in the other container?

Answer 1

In order to determine the gradient of line P, we need to find the change in the amount of water (in litres) in container P for a given change in time. The gradient represents the rate of change.

(a) To calculate the gradient of line P, you need to choose two points on the line and find the change in the amount of water divided by the change in time. Let's say you choose the points (0, 60) and (5, 20) on the graph, where 0 represents the starting time and 5 represents some time later:

Gradient of P = (Change in Water) / (Change in Time) = (60 - 20) / (5 - 0) = 40 / 5 = 8 liters per hour

So, the gradient of line P is 8 liters per hour.

(b) (i) To determine which container will become empty first, you need to look at the gradient. The container with the steeper gradient will empty faster because it's losing water at a faster rate. In this case, container P has a gradient of 8 liters per hour, and container Q's gradient is not given. You'll need to find the gradient of line Q to compare.

(ii) Once you have the gradient for line Q, you can calculate how much water is left in the other container when one becomes empty by using the formula:

Amount of water left = Initial amount of water - (Gradient * Time)

Please provide the gradient of line Q or any additional information about it, and I can help you find the answer to part (b)(ii).