Astudent on the cross-country team runs 30 minutes a day as a part of her training,
write an equation to describe the relationship between the distance she runs in miles, d, and her
running speed, in miles per hour, when she runs:
(unit 2. lesson 2)
a.
at a constant speed of 4 miles per hour for the entire 30 minutes
b.
at a constant speed of 5 miles per hour the first 20 minutes, and then at 4 miles per hour the
last 10 minutes
at a constant speed of 6 miles per hour the first 15 minutes, and then at 5.5 miles per hour for
the remaining 15 minutes
d. at a constant speed of a miles per hour the first 6 minutes, and then at 6.5 miles per hour for
the remaining 24 minutes
e. at a constant speed of 5.4 miles per hour form minutes, and then at b miles per hour forn
minutes

Step-by-step explanation:

In this problem, the student is running at a constant speed, which is the center of the problem, because that allow us to use the mathematical relation between speed, distance and time, in a constant movement. It's important to say that constant movement refers to the absence of acceleration, that it, the speed doesn't change. So, the general relation is set by the equation:

First, all magnitudes must have same units, there cannot be hours and minutes at the same time, so we'll transform 30 minutes in to hours. For that purpose, we know that 1 hour equals 60 minutes. Therefore, 30 minutes is half an hour, or 0.5 hours, then:

So, the student runs 2 miles.

In this case, we have two movements.

We need to transform minutes into hours:

Now, we can the expressions and calculate the distances:

First movement:

Second movement:

So, the student ran 2.33 miles in total.

Same processes.

First movement:

Second movement:

Therefore,  the student ran 2.88 miles in total.

First movement:

Second movement:

The student ran (0.10a + 2.6) miles.

First movement:

Second movement:  

Therefore, the student ran (0.09m + (bn/60)) miles.

the answer for this question is 38