1. Elena works out on a treadmill. She uses a program that combines running and walking, She knows that she runs at 0.2 miles per minute and she walks at 0.1 miles per minute. At the end of her workout, the treadmill showed her workout distance was 8 miles. a. **Give three possible combinations of walking and running times that would result in Elena having a workout distance of 8 miles.

The three possible combinations are:

1. Running for 30 minutes, walking for 20 minutes

2. Running for 35 minutes, walking for 10 minutes

3. Running for 25 minutes, walking for 30 minutes

Step-by-step explanation:

Given that:

Elena combines running and walking on a treadmill.

Running speed = 0.2 miles/hr

Walking speed = 0.1 miles/hr

Total distance traveled = 8 miles

To find:

Three possible combinations of walking and running times.

Solution:

First of all, let us have a look at the formula for distance traveled:

Distance = Speed Time

Here, we are given that the distance is 8 miles which is covered by both running and walking.

Let the time taken in running = minutes

Let the time taken in walking = minutes

Distance traveled by running = miles

Distance traveled by walking = miles

As per question statement:

Now, we need to find 3 set of solutions for above equation.

The solutions can be:

x = 30, y = 20

x = 35, y = 10 and

x = 25, y = 30

So, the three possible combinations are:

1. Running for 30 minutes, walking for 20 minutes

2. Running for 35 minutes, walking for 10 minutes

3. Running for 25 minutes, walking for 30 minutes

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3