Wednesday, Thursday, Feb 12-13, Applications Involving Rational Equations

Post date: Feb 13, 2014 9:54:22 PM

Notes:

Let's look at this question:

A boat travels at a constant speed of 3 miles per hour in still water. In a river with unknown current, it takes the boat twice as long to travel 60 miles upstream (against the current) than it takes for the 60 miles return trip (with the current. ) What is the speed of the current in the river?

The equations for rate(r), distance(d), and (t) are: d=rt. r=d/t, t=d/r

  • Let c= speed of the current

Let's make a table to see what we know so far:

Note that each row of table 1 has two entries entered. The third entry in each row is time.The relation t=d/v can be used to compute the time entry in each row of table 1.

For example, in the first row, d=60 miles and r=3-c miles per house. Therefore, the time of travel is

Now, we can complete the table:

To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. This leads to the result

Example:

1. Bill can finish a report in 2 hours. Maria can finish the same report in 4 hours. How long will it take them to finish the report if they work together?

In this case, we need to use the equation: Rate=work/time=1 report/t h

2. It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. Together, they can complete the same job in 12 hours. How long does it take Hank to complete the job if he works alone?

  • Let H=the time it take Hank to complete the job of painting the kitchen when he works alone.

Thus, Hank is working at a rate of 1/H kitchens per hour. Similarly, Liya is working at a rate of 1/(H+7) kitchens per hour. Because it takes them 12 hours to complete the task when working together, their combined rate if 1/12 kitchens per hour.

Homework:

Application Involving Rational Equations Worksheet Due tomorrow