Rational Equations Quiz

Working alone, it would take Shandra 40 minutes to sand a table. To sand the same table, also working alone, it would take Kelly 1 hour. If they work together, the situation can be modeled by the following equation, where t is the time it would take to sand the table working together.Shandra claims it will take them about 50 minutes working together, because 50 is the mean of 40 and 60. Which best describes Shandra's claim?

Shandra's estimate is too high because it will take them about 24 minutes.

Which of the following represents the solution of 3/2=3/2x-6/5x

x=1/5

A student solves the following equation for all possible values of x:His solution is as follows:Step 1: 8(x - 4) = 2(x + 2)Step 2: 4(x - 4) = (x + 2)Step 3: 4x - 16 = x + 2Step 4: 3x = 18Step 5: x = 6He determines that 6 is an extraneous solution because the difference of the numerators is 6, so the 6s cancel to 0.Which best describes the reasonableness of the student's solution?

His solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.

What causes a solution to a rational equation to be an extraneous solution?

If a solution results in zero when substituted into the denominator of the equation, the solution is extraneous.

Yumi and Juan pick up litter along the highway at the same rate. Yumi picks up litter for 3 miles and takes 2 hours longer than Juan, who picks up litter for 2 miles. If Juan spent x hours picking up litter, the following equation models the situation.

6 hours

What is the solution to the equation -3d/d^2-2d-8+3/d-4=-2/d+2?

d=1

What is the solution to the equation 1/h-5+2/h+5=16/h^2-25?

h=7

What is the solution to the equation 3/m+3-m/3-m=m^2+9/m^2-9?

no solution

What are the solutions to the equation w/2w-3=4/w?

w=2 and w=6

What is true about the solution of x^2/2x-6=9/6x-18?

x=+/-{sqrt}3, and they are actual solutions