Question

A vehicle travels 55 miles per hour and 20 miles per gallon.

a. Write an equation that represents the distance d (in miles) that the vehicle travels in t hours. Then write an equation that represents the distance d (in miles) that the vehicle travels using g gallons of gasoline.
b. Write an equation that relates g and t. Then solve the equation for g.
c. Thevehicletravelsfor6hours.Howmanygallons of gasoline does the vehicle use? How far does it travel? Explain.

Answer 1

Explanation:

The distance d (in miles) you travel in a car is given by d=55t where t is the time (in hours)

The distance d (in miles) you travel in a car is given by d=20g where g is the number of gallons of gasoline the car uses.

1. Write an equation that relates g & t.

20g=55t20g=55t

2. Solving for g.

20g=55t20g=55t

=> g=\frac{55t}{20}g=

20

55t

Hence, g= 2.75tg=2.75t

3. You travel for six hours. How many gallons of gasoline does the car use

We will use this equation g= 2.75tg=2.75t to solve the question.

Putting t = 6

g= 2.75(6)g=2.75(6)

g = 16.5 gallons

4. How far do you travel?

We can use equation d=55td=55t here

d=55\times6=330d=55×6=330 miles