Science:Math Exam Resources/Courses/MATH104/December 2012/Question 05 (a)/Solution 1
Consider a 15ft tall lamp at the origin of a grid (so that everyone to the right is a positive distance away and everyone to the left is a negative distance away).
Let x be the distance that Alice is to the left of the lamp. We know that she is 5ft tall (which is shorter than the lamp post). Next, let y be the distance that Bob is to the right of the lamp. He is 6ft tall and so he is also shorter than the lamp but slightly taller than Alice.
Rays of light will shine from the lamp, touch Alice and Bob and eventually reach the ground (forming a big triangle with the lamp and ground). Label the distance between where the light hits the ground for Alice and the lamp as C and for Bob, D.
With this notation then the length of Alice's shadow, for example, should be C-x. To get a better understanding of how we could see the geometry of the problem better and how to go about solving it, it is often useful to simplify the diagram. To do this we will replace our characters with sticks since their dimensions don't affect the problem as far as we are concerned. An example of what a more mathematically-ready diagram should look like is below:
The distance between the tips of the shadows is C+D and since we know this is decreasing at 11ft/s, we could write
