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Expert-verified Found in: Page 133 ### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776 # Driving A family is driving to Houston, Texas. A sign indicates that they are 700 miles from Houston. Their car’s trip odometer indicates that they are 400 miles from home. They are travelling at an average speed of 60 miles per hour.Write an expression for the distance (in miles) they will be from Houston in x hours.Write an expression for the distance (in miles) they will be from home in x hours.Use the expression from parts a and b to write and solve an equation to find the number of hours they will drive until they are exactly halfway between Houston and their home.Suppose they travel by local roads instead of highway. They travel the 700 miles at a speed of 45 miles per hour. How long will they drive before they are exactly halfway between Houston and their home?

(a) An expression for the distance is $1100-60x.$

(b) The distance from home in x is $60x$miles.

(c) The number of hours is $x\text{=9.16}$.

(d) $6.6+3.3=9.9\approx 10$hours.

See the step by step solution

## a.Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

## Step-2 – Given information

They are 700 miles from Houston, they are 400 miles from home and they are travelling at an average speed of 60 miles per hours.

## Step-3 – Find the expression

Total distance between Houston and the home is $700+400=1100$ miles. The speed is 60 mph and therefore the distance travelled in x hours is $60x$ and this implies that the distance from Houston in x hours will be given by the expression $1100-60x.$

Hence, an expression for the distance is $1100-60x.$

## b.Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

## Step-2 – Given information

They are 700 miles from Houston, they are 400 miles from home and they are travelling at an average speed of 60 miles per hours.

## Step-3 – Find the expression

The time-distance formula is given by

$\text{Distance}=\text{Speed}×\text{Time}$

The speed is 60mph and therefore the distance travelled or distance from home in x is 60x miles.

Hence, the distance from home in x is $60x$ miles.

## c.Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

## Step-2 – Given information

They are 700 miles from Houston, they are 400 miles from home and they are travelling at an average speed of 60 miles per hours.

## Step-3 – Find the expression

Therefore, the number of hours to drive until exactly halfway between Houston and home is: $60x=1100x-60x$

Rearrange:

$\begin{array}{l}⇒60x+60x=1100\\ ⇒120x\text{=1100}\\ ⇒\text{}x\text{=}\frac{1100}{120}\\ ⇒\text{}x\text{=9.16}\end{array}$

Hence, the number of hours is $x\text{=9.16}$.

## d.Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

## Step-2 – Given information

They are 700 miles from Houston, they are 400 miles from home, they are travelling at an average speed of 60 miles per hours and they travel the 700 miles at a speed of 45 miles per hours.

## Step-3 – Find the expression

Halfway between the house and Houston is 550 miles from the house. they first 400 miles are travelled at a speed of 60mph which took $\frac{400}{60}=6.6$ hours. The remaining $550-400=150$ are not to be driven at 45 mph, which should take another $\frac{150}{45}=3.3$ hours . therefore the total time required to be exactly halfway between house and Houston according to the given situation is $6.6+3.3=9.9\approx 10$ hours. ### Want to see more solutions like these? 