STANDARD 15:
RATE, WORK & MIXTURE WORD PROBLEMS
Distance Word Problems
"Distance" word problems, often also called "uniform rate" problems, involve something travelling at some fixed and steady ("uniform") pace ("rate" or "speed"), or else moving at some average speed. Whenever you read a problem that involves "how fast", "how far", or "for how long", you should think of the distance equation, d = rt, where d stands for distance, r stands for the (constant or average) rate of speed, and t stands for time.Warning: Make sure that the units for time and distance agree with the units for the rate. For instance, if they give you a rate of feet per second, then your time must be in seconds and your distance must be in feet. Sometimes they try to trick you by using the wrong units, and you have to catch this and convert to the correct units.
Another Distance Example
A train leaves Deb's house and travels at 50 miles per hour. Two hours later, another train leaves from Deb's house on the track beside or parallel to the first train but it travels at 100 miles per hour. How far away from Deb's house will the faster train pass the other train?
Remember, d will represent the distance in miles from Deb's house and t will represent the time that the slower train has been travelling.
It is helpful to draw a diagram to show what is happening, see the Train Diagram image.
Organize the information you have in a chart if you haven't solved these types of problems before. Organize your chart by giving the equation information and the formula:
distance= speed x time
.See the image.
Now you can solve the system of equations:
50t = 100 (t - 2)
50t = 100t - 200
200 = 50t
t = 4
Now substitute t = 4 into train 1
d =50t
=50(4)
=200
Now you can write your statement. "The faster train will pass the slower train 200 miles from Deb's house.
Remember, d will represent the distance in miles from Deb's house and t will represent the time that the slower train has been travelling.
It is helpful to draw a diagram to show what is happening, see the Train Diagram image.
Organize the information you have in a chart if you haven't solved these types of problems before. Organize your chart by giving the equation information and the formula:
distance= speed x time
.See the image.
Now you can solve the system of equations:
50t = 100 (t - 2)
50t = 100t - 200
200 = 50t
t = 4
Now substitute t = 4 into train 1
d =50t
=50(4)
=200
Now you can write your statement. "The faster train will pass the slower train 200 miles from Deb's house.
Work Word Problems
"Work" problems involve situations such as two people working together to paint a house. You are usually told how long each person takes to paint a similarly-sized house, and you are asked how long it will take the two of them to paint the house when they work together. Many of these problems are not terribly realistic (since when do two laser printers work together on printing one report?), but it's the technique that they want you to learn, not the applicability to "real life".
The method of solution for work problems is not obvious, so don't feel bad if you're totally lost at the moment. There is a "trick" to doing work problems: you have to think of the problem in terms of how much each person / machine / whatever does in a given unit of time.
For instance:
The method of solution for work problems is not obvious, so don't feel bad if you're totally lost at the moment. There is a "trick" to doing work problems: you have to think of the problem in terms of how much each person / machine / whatever does in a given unit of time.
For instance:
Mixture Word Problems
Mixture problems involve creating a mixture from two or more things, and then determining some quantity (percentage, price, etc) of the resulting mixture.
The easiest way to solve these problems is also a grid.
The easiest way to solve these problems is also a grid.
Watch this helpful example: http://www.virtualnerd.com/algebra-1/linear-equations-solve/volume-of-soluton-from-percent-example.php
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