# Question #82836

Oct 15, 2016

The rate before lunch = 40 miles/ hour

#### Explanation:

$2 \times x + 3 \times \left(x + 10\right) = 230$

where $x =$the rate before lunch
$2 x =$ the distance traveled by the rate for two hours.

where $\left(x + 10\right) =$ the rate after lunch.

$3 \left(x + 10\right) =$ the distance travel by that rate for three hours.

$230 =$ the total distance traveled.

Solve the equation for x will give the rate before lunch

$2 \times x + 3 \left(x + 10\right) = 230$ first multiply across the parenthesis using the distributive property. This gives.

$2 x + 3 x + 30 = 230$ Now use the associate property to add the like terms $2 x + 3 x = 5 x$ so

$5 x + 30 = 230$ subtract 30 from both sides gives

$5 x + 30 - 30 = 230 - 30$ This results in

$5 x = 200$ divide both sides by 5

$\frac{5 x}{5} = \frac{200}{5}$ The answer is

$x = 40$