Example
Superman took 24 hours to travel 10,000 miles with the wind. The return trip was in the opposite direction of the wind and took 40 hours. Remember, Superman can fly faster than a speeding bullet (and Superman can fly faster than the wind). What was the speed of the wind?
a) Identify the unknown and assign a variable to each.
b) Write the system of equation(s)
c) Solve the system of equation(s), and give your answer as an ordered pair.
d) Write a sentence answering the question above.
solution
a) The problem involves two trips, one with the wind, and one against the wind. In both cases, the distance was 10,000 miles. However, the time differs depending on the wind. Going in the same direction with the wind, making him go faster and going against the wind, making him go slower. Superman going against the wind took 40 hours. So the only unknowns are the rates: Superman's speed and the wind's speed.
S: Superman's Speed
W: The Wind's Speed
W: The Wind's Speed
b) The trip there, the total is S+W since the wind is going in the same direction as Superman, we add them together. The return trip, the wind is going the opposite direction that Superman is going, so we subtract them to get the rate S-W. Using the formula D=RT, we get the following system of equations, one for the trip there and one for the return trip.
c) To solve the system of equations, you distribute the time and then use elimination. But, in this case, the coefficients divides evenly on both sides, so first divide the coefficients. So, for the first equation, divide both sides by 24 and the second equation by 40. Then, we get the simplified system of equations
Our system of equations now are set up for elimination since the W variables have opposite coefficients. Adding the two equations together, we get:
This can be easily simplified by dividing by 2 getting 333.3 miles per hour
We have found the S value. Now we need to find the W value. TO do so, we substitute out value for S into any previous equation involving S and W, then for W getting us 83.3 miles per hour.
Our ordered pair is written out as:
d) The speed of the wind would be going 83.3 miles per hour.
EQUATION, TABLE, AND GRAPH
reflection
This example is about the speed of the wind is going when Superman is flying against the wind. The word problem gives the information that it takes 24 hours for Superman to fly 10,000 miles with the wind and 40 hours for Superman to fly 10,000 miles against the wind. The system of equations is a collection of two or more equations with a same set of unknowns in solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. The unknowns for this world problem is 'S' for Superman's speed and 'W' for the wind's speed. With the 'S' or 'W' value that was found, you substitute the values to any previous equation involving 'S' and 'W'. This world problem is a easy going by having a simple multi-step solution, but not so easy that it wouldn't take five minutes to solve. The graph depicts two lines that show how fast Superman is going with or against the wind and intersecting at some point. Overall the word problem is another good step forgetting well verse with dealing more advance problems with more variables.