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2 years ago

17. Distance to Work Johnny gets to work in 20 minutes

Mathematics

1 answer:

Marrrta [24]2 years ago

6 0

Answer:

2.25 miles

Step-by-step explanation:

When driving a car time taken is 20 minutes. This is equal to 20/60 hours , 1/3 hours / 0.3 hours

When riding a bike , time taken is 45 minutes. This is 45/60 hours , 3/5 hours/ 0.75 hours

The formula for speed is : Speed = Distance covered / time taken

The statement is that the driving speed is greater than biking speed by 4.5 mph

Assuming the distance to work is x miles then;

x/ 0.3 - x/0.75 = 4.5 ------eliminate 0.3 by multiplying each term by 0.3 to get

x- 0.3/0.75 x = 1.35 -------eliminate 0.75 by multiplying each term by 0.75 to get

0.75 x - 0.3 x = 1.0125

0.45 x = 1.0125

x= 1.0125 / 0.45

x = 2.25

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3 years ago

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit

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Changing the equation into slope form: $y = mx + c$ , where $m$ is the slope [gradient] and $c$ is the y-intercept.

$2x+3y=1470$
$3y = -2x+1470$
$y= - \frac{2}{3}x+ \frac{1470}{3}$
$y=- \frac{2}{3}x+490$

The gradient is $- \frac{2}{3}$ and y-intercept is at $y=490$

Graphing $y=- \frac{2}{3}x+490$ using slope-intercept method:
a) The slope is a negative slope. The line will go 'down hill'
b) The line must pass the point (0, 490)
c) The line will intercept the x-axis at y = 0
   $0 = - \frac{2}{3}x+490$
   $\frac{2}{3}x = 490$
   $2x = 1470$
   $x = \frac{1470}{2}$
   $x = 735$
So, x-intercept is at (735, 0)

The graph of this function is shown below. The intercepts are labelled at:
y = 490
x = 735

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Next month's profit equation

$2x+3y=1593$

Rewriting this into slope-equation form

$3y = -2x+1593$
$y=- \frac{2}{3}+ \frac{1593}{3}$
$y= - \frac{2}{3}+531$

The gradient, $m$ , equals to $- \frac{2}{3}$
The y-intercept, $c$ , equals to 531

The equation still has the same gradient with last month's profit equation but different y-intercept.

-------------------------------------------------------------------------------------------------------------

A linear graph show points of (0, 300) and (450, 0)

We work out the slope:
$\frac{300-0}{0-450} = \frac{300}{-450}=- \frac{20}{30} =- \frac{2}{3}$

Y-intercept at x = 0, so it's at y = 300

Equation $y = - \frac{2}{3}+300$