Distance, Rate & Time
Example: On a jog you walk at 5mph for a while and then at 8mph. In total you run 7 miles in 1.1 hours. How long did you run each walk?
This can be interpreted as:
and resolve to . This leads to the equation which can be solved for where represents the time taken for one walk and represents the time taken for the other walk.
You travel in a car from town A to town B at an average speed of 64km/h. On the return journey your average speed is 80km/h. You take 9 hours in total.
How far is it from A to B?
implies . Since we know the rates of both trips and their total time, an equation can be derived that has the distance as its only unknown:
equals to % of .
A number plus 4% of itself is 41.6. Find that number. This implies:
Celsius & Fahrenheit
Given a known Fahrenheit value, its Celsis equivalent can be found by solving the formula for . For 86 degrees Fahrenheit to Celsius:
Various word problems involving algebra.
A man is 4 times as old as his son. In 4 years time he will be three times as old. How old are both now?
This problem is somewhat ambiguous. In 4 years time the man will be three times as old as what? Plugging in values for their ages helps finding the correct equations.
Age of man:
Age of man in 4 years:
Example of Problem involving Quadratic Equations
A watermelon falls from a 225ft tall building. How long does it take the melon to hit the ground level? The height of the watermelon is given by the following formula:
The goal is to find when . This implies the quadratic equation:
That can be solved for and . Given the context cannot be a negative, therefore is the solution to the problem.