CPhill

The diagonal of a square is √2 times as long as the length of a side.

So, dividing the diagonal length by √2, we have that the side is just 7 inches.

8x+y=-16

-3x+y=-5          Multiply the second equation by -1 and add it to the first equation

This gives

11x = =11        Divide both sides by 11

x = -1              

Now...just substitute this into either equation to find y......I'll use the first one

8(-1) + y = -16

-8 + y = -16       Add -8 to both sides

y = -8

Check both answers in the second equation

-3(-1) - 8 = -5

3 - 8 = -5

Yep...that works....!!!!

Factor the "y" out on the left side

y(k + q) = t      Divide both sides by (k + q)

y = t / (k + q)

Remember that we can write 32 as 16*2

So.......

√32 = √(16*2) = √16 * √2  = 4√2

3√2 - √2 = 2√2

We can set this up as a proportion.

Let the longest side of the smaller triangle = x

Let the longest side of the larger triangle = x + 3

And they're in a 5:4 ratio

So we have

(x+3)/x = 5/4    Cross-multiply

4(x+3) = 5x

4x + 12 = 5x    Subtract 4x from both sides.

12 = x      And this is the longest side of the smaller triangle.

x + 3 = 15    And this is the longest side of the larger triangle.

......You might be right!!!......

"Fossils" have a limited shelf life.......

Don't get too cocky, you whippersnappers!!!.....the "fossil" still has a few tricks up his sleeve.......

OK...I was trying to beat GL......but that seems impossible, tonight....let me explain step by step

You were running at 8 mph, but you increased it to 10 mph.

So in 60 minutes, you can run 10 miles. The question becomes, how long will it take you to run 6.2 miles??  So, setting it up as a proportion we have

t/6.2 = 60/10    where t is the time it takes to finish the 6.2 miles.....

And as we saw, that was .62hrs.....this should make sense, it should take less time to run 6.2 miles than it does to run 10 miles....

Now, to find out how long it took you to run the first 20 miles, we have

D/R = T

So

(20 miles) / (8mi/hr) = 20hr/8 = 2.5 hrs.

And 2.5 + .62 = 3.12 hrs.

Does that make sense???

So, the last 6.2 miles you ran at 10mph...we can solve this usung a proportion

t/6.2 = 60/10   where t is the number of minutes you take to finish

t/6.2 = 6

t = 6(6.2) = 37.2 min = .62 hrs

So the time it took you to run the first 20 miles is given by

D/R =T      20/8 = 2.5 hrs

Add this to the time it took to run the last 6.2 miles and we have

2.5 + .62 = 3.12 hrs.

So you finished ahead of your friend.....