SOLUTION: Hi. I am having difficulty setting up this problem since there are many variables. Here is the question: A tourist travels 1500 miles using two planes. The second plane averag

Algebra ->  Equations -> SOLUTION: Hi. I am having difficulty setting up this problem since there are many variables. Here is the question: A tourist travels 1500 miles using two planes. The second plane averag      Log On


   

Question 706866: Hi. I am having difficulty setting up this problem since there are many variables.
Here is the question:
A tourist travels 1500 miles using two planes. The second plane averages 50 miles per hour faster than the first plane. The tourist uses the slower plane for the first 500 and the faster plane for the next 1000 miles. The total flying time is 6.5 hours. What is the speed of the first plane?
Speed of first plane = ______ mph
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Create a table of data information. Assigning r for speed of the slower, first plane, and then r+50 for the speed of the second, faster plane, we can show this:

Plane____________speed mph________time in hours_________distance miles
First____________r__________________(___)________________500
Second__________r+50________________(___)_______________1000
TOTAL______________________________6.5__________________1500

Some information seems to be missing but we can fill in the missing parts.
speed*time=distance. This is equivalent to time=(distance)/(speed).

Put in the missing information:
Plane____________speed mph________time in hours_________distance miles
First____________r__________________%28500%2Fr%29________________500
Second__________r+50________________%281000%2F%28r%2B50%29%29_________1000
TOTAL______________________________6.5____________________1500

We KNOW how much fly time was used and we can ADD individual time expressions to get the total time, so if we do it: %28500%2Fr%29%2B1000%2F%28r%2B50%29=6.5, we can solve for r, the only variable, the speed of the slow plane, from which we can also find the speed of the faster plane.