Question

Solve using a proportion: If Leigh Ann can drive 60 miles in 1.5 hours, how many miles will she drive in 3 hours?

a) 80 miles
b) 90 miles
c) 120 miles
d) 160 miles

Answer 1

(c)

Step-by-step explanation:

Distance ( D), speed (S) and time (T) are related by

S =
`(D)/(T)` ( S is constant )

let x be the distance travelled in 3 hours , then by proportion

`(60)/(1.5)` =
`(x)/(3)` ( cross multiply )

1.5x = 3 × 60 = 180 ( divide both sides by 1.5 )

x = 120

She drives 120 miles in 3 hours

Answer 2

Leigh Ann will drive
`120 miles` in
`3 hours` based on the proportion that relates the number of miles driven to the number of hours by setting up a proportion and solving for the unknown value.

Step-by-step explanation:

To solve using a proportion for how many miles Leigh Ann will drive in 3 hours, based on driving
`60 miles` in
`1.5 hours`, we can set up the proportion as follows:

• Let x represent the number of miles driven in
  `3 hours`.
• The ratio of miles to hours for the given situation is
  `60 miles/1.5` hours, which should be equal to
  `x miles/3 hours`.

Setting up the proportion gives us:

`\(\frac{60 \text{ miles}}{1.5 \text{ hours}} = \frac{x \text{ miles}}{3 \text{ hours}}\)`

To solve for x, let's cross-multiply and divide as shown:

1. Multiply both sides of the equation by 3 hours to get rid of the denominator on the right side.
2. 
   `(60 miles * 3 hours) / 1.5 hours = x miles`
3. 
   `x = (60 * 3) / 1.5`
4. 
   `x = 180 / 1.5`
5. 
   `x = 120 miles`

Next, check whether the answer is reasonable. If Leigh Ann drives

`60 miles` in
`1.5 hours`, it's logical that she would drive twice as far in double the time, which is 3 hours. Therefore, driving
`120 miles` in
`3 hours` makes sense and is the correct answer, which corresponds to option c).