Question

related questions: lesson 6: common algebra word problems

type the answer in the box, rounding to the nearest tenth place.

q. frank and dave started driving at the same time from the same place. they went in the same direction, but frank drove at an average speed of 45 miles per hour and dave drove 55 miles per hour. how many hours did it take them to be 25 miles apart? (hint: dave will drive 25 miles farther than frank. the difference in the distances will be 25 miles.)

Explanation:

Define variables and expressions

Using the Translating Word Problems knowledge point
Let \(t\) represent the time in hours that Frank and Dave drive.
The distance Frank drives is:

$$d_{\text{Frank}} = 45t$$

The distance Dave drives is:

$$d_{\text{Dave}} = 55t$$

Set up the distance equation

Using the Translating Word Problems knowledge point
The difference in their distances is 25 miles:

$$55t - 45t = 25$$

Solve for time

Using the Solving Multi-Step Equations knowledge point

$$
LATEXBLOCK0
$$

Round to the nearest tenth

Using the Translating Word Problems knowledge point
The value \(2.5\) is already at the tenths place.

$$t = 2.5$$

Answer:

Frank and Dave started driving at the same time from the same place. They went in the same direction, but Frank drove at an average speed of 45 miles per hour and Dave drove 55 miles per hour. How many hours did it take them to be 25 miles apart? (Hint: Dave will drive 25 miles farther than Frank. The difference in the distances will be 25 miles.) <blank>2.5</blank>