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Jun 12, 2019
edited by sinclairdragon428  Nov 20, 2019

#1
+2

2. Adam ran across the field at a speed of 5 yards per second and walked back along the same path at a speed of 2 yards per second. For how many seconds did he run if the total round-trip time was three and a half minutes?

3 1/2 minutes  = 3 min 30 sec =   210 sec

Call the distance across the field D

And   Distance / Rate  = Time  ...so..

Time Running + Time Walking  = Total Time.

D / 5  +   D / 2   =  210

2D + 5D

________   =   210        multiply through by  10

10

7D  =  2100    divide both sides by  7

D = 300 yards

So....the time walking  =  300/2 = 150 sec =  2 min 30 sec

And the time running = 300/5  = 60 sec =  1 minute   Jun 12, 2019
#2
+1

********   Jun 12, 2019
edited by CPhill  Jun 12, 2019
#4
-2

It says 10√6 is incorrect, do you know where you went wrong?

sinclairdragon428  Jun 12, 2019
#6
+3

$$y\ =\ \frac{15\sqrt{24}}{\sqrt{x}}$$

What is  x  when  y = 3 ?  Plug in  3  for  y  and solve for  x .

$$3\ =\ \frac{15\sqrt{24}}{\sqrt{x}}$$

To solve for  x ,

divide both sides of the equation by  15

then square both sides of the equation

then multiply both sides of the equation by  x

then multiply both sides of the equation by  $$\frac{225}{9}$$

Can you do those things sinclairdragon?  If you get stuck let us know! hectictar  Jun 12, 2019
#7
0

I got to 1/25x = \sqrt24 but i'm not sure where to go from there.

sinclairdragon428  Jun 12, 2019
#8
+1

$$3\ =\ \frac{15\sqrt{24}}{\sqrt{x}}$$

Divide both sides of the equation by  15

$$\frac{3}{15}\ =\ \frac{\sqrt{24}}{\sqrt x}$$

Square both sides of the equation.

$$\Big(\frac{3}{15}\Big)^2\ =\ \Big(\frac{\sqrt{24}}{\sqrt x}\Big)^2$$

Simplify both sides using the rule  $$\big(\frac{a}{b}\big)^2\ =\ \big(\frac{a}{b}\big)\big(\frac{a}{b}\big)\ =\ \frac{a^2}{b^2}$$

.$$\frac{3^2}{15^2}\ =\ \frac{(\sqrt{24}\,)^2}{(\sqrt x\,)^2}$$

$$\frac{9}{225}\ =\ \frac{24}{x}$$

Now multiply both sides of the equation by  x

$$x\cdot\frac{9}{225}\ =\ 24$$

Multiply both sides of the equation by  $$\frac{225}{9}$$

$$x\cdot\frac{9}{225}\cdot\frac{225}{9}\ =\ 24\cdot\frac{225}{9}$$

$$x\ =\ 24\cdot\frac{225}{9}$$

$$x\ =\ 600$$

hectictar  Jun 12, 2019
#3
+2

3. Suppose a is jointly proportional to b and c. If a=4 when b=8 and c=9, then what is a when b=2 and c=18.

a = kbc

4 = k(8)(9)

4 = k (72)

4/72  = k  = 1/18

a = (1/18)(2)(18)  =  2   Jun 12, 2019
#5
-1

Thanks!

sinclairdragon428  Jun 12, 2019