Chapter 8.3, Problem 18IP

(a)

To determine

Make a table to show how many gallons of gasoline are remaining in the tank after each hour.

Answer to Problem 18IP

Remaining amount of gasoline in gallons / hour: $40/0;33/1;26/2;19/3;12/4;5/5;$

Explanation of Solution

Given:

At the start of the school trip to Washington D.C, the tour bus has 40 gallons of gasoline in the fuel tank. Each hour, the bus uses 7 gallons of gasoline. The bus will stop for gas when there are 10 gallons left.

Make a table to show how many gallons of gasoline are remaining in the tank after each hour.

Concept Used:

The tour bus has 40 gallons of gasoline in the fuel tank. Each hour, the bus uses 7 gallons of gasoline.

So to find the remaining amount of gasoline in the tank, we need to subtract 7 from the remaining amount after each hour.

Calculation:

After each hour	0 hour	At 1st hour	At 2nd hour	At 3rd hour	At 4th hour	At 5th hour
Gasoline left in the fuel tank in gallons	40	40 − 7 = 33	33 − 7 = 26	26 − 7 = 19	19 − 7 = 12	12 − 7 = 5

Thus, remaining amount of gasoline in gallons / hour: $40/0;33/1;26/2;19/3;12/4;5/5;$

(b)

To determine

Write and solve an equation to find how many hours will pass before the bus will have to stop for gasoline.

Answer to Problem 18IP

The bus will stop for gas after 4 hours 17 min of running when there are 10 gallons left.

Explanation of Solution

Given:

At the start of the school trip to Washington D.C, the tour bus has 40 gallons of gasoline in the fuel tank. Each hour, the bus uses 7 gallons of gasoline. The bus will stop for gas when there are 10 gallons left.

Write and solve an equation to find how many hours will pass before the bus will have to stop for gasoline.

Concept Used:

Let x be the number of hours passed. Since the bus consumes 7 gallons for each hour, then multiply it by x to 7. Next Since the Total capacity is 40 gallons; subtract 7x from 40 indicating the number of gallons remaining in the tank.

Calculation:

The bus will stop for gas when there are 10 gallons left.

The required equation: $40-7x=10$

Now solve for x:

  $\begin{array}{l}40-7x=10\\ 40-40-7x=10-40[\text{Subtract40}\text{from}\text{both}\text{sides}]\\ -7x=-30\\ \frac{-7x}{-7}=\frac{-30}{-7}[\text{Divide}\text{each}\text{side}\text{by}-7]\\ x=4\frac{2}{7}\text{hours}=4\text{hours}17\min \end{array}$

Thus, the bus will stop for gas after 4 hours 17 min of running when there are 10 gallons left.