Question

Please help with #12

Answer 1

Answer:

a. 1 1/8 b. 8/9

Step-by-step explanation:

You can set this up as a proportion to solve.  For part a. we know that 2/3 of the road is 3/4 mile long.  2/3 + 1/3 = the whole road, so we need how many miles of the road is 1/3 its length.  Set up the proportion like this:

$\frac{\frac{2}{3} }{\frac{3}{4} } =\frac{\frac{1}{3} }{x}$

Cross multiplying gives you:

$\frac{2}{3}x=\frac{1}{3}*\frac{3}{4}$

The 3's on the right cancel out nicely, leaving you with

$\frac{2}{3}x=\frac{1}{4}$

To solve for x, multiply both sides by 3/2:

$\frac{3}{2}*\frac{2}{3}x=\frac{1}{4}*\frac{3}{2}$ gives you

$x=\frac{3}{8}$

That means that the road is still missing 3/8 of a mile til it's finished.  The length of the road is found by adding the 3/4 to the 3/8:

$\frac{3}{4}+\frac{3}{8}=\frac{6}{8}+\frac{3}{8}=\frac{9}{8}$

So the road is a total of 1 1/8 miles long.

For b. we need to find out how much of 1 1/8 is 1 mile:

1 mile = x * 9/8 and

x = 8/9.  When 1 mile of the road is completed, that is 8/9 of the total length of the road completed.