TL;DR (Too Long; Didn't Read)
A) A variable is a letter being substituted for an unknown number to help solve for it. W+B=36 miles, where W is a variable for Walking Distance and B is a variable for Biking Distance
B) 2 hours biking and 3 hours walking
HUGE VERY HELPFUL EXPLANATION YOU SHOULD PROBABLY READ:
A variable can be any letter you want to be used in place of something you don't know. We use variables to help us to solve equations. For example, what if you didn't know "what" plus 4 made 9? Well, of course you know the answer, but this is a simple demonstration to show an example of how they'd be used. You pick any letter from the alphabet (most people use X by default.. so I will use it too.) and place it where you don't know what would go there. In this example equation, it would look like this: 4+x=9. It's like changing something that REQUIRES words to explain into math so that it doesn't need words to explain it anymore. Notice how when I gave the example, I used quotation marks around what? Well "what" is X in this equation, which is how we used a letter in math to remove the need for words. (Basically to solve it you'd get everything you know to one side, by solving, which would come out to be 9-4=x [one side] and solved using subtraction to get 5=x [solved after moving to one side])
TO THE WORK:
A) Define a variable and write an equation for this situation.
Variable defined, done. Next is the equation.
We'll use W as a variable for Walking Distance and B as a variable for Biking Distance.
Equation to A: W+B=36miles
B) How many hours did Tyrell spend on each activity?
Next, the problem also gave us the rates at which Tyrell walked/biked, and told us he walked for one more hour than he biked.
We take the total distance and divide it by 12 to get the total amount of biking he COULD'VE done, then redo it for 4 to get the total amount of walking he COULD'VE done.
36/12=3
36/4=9
We also know he couldn't have done the maximum amount of either, as we're given the information that he walks one more hour than he bikes. This in itself is another equation, we'll use W and B again, Wt for WalkTime and Bt for BikeTime.
Wt=Bt+1 -- Because we KNOW he walked one more hour than he biked, so we can take the biking hours he did and add one to it to get the amount of time he walked.
He couldn't have biked 3 hours because that's the total distance, meaning he wouldn't have walked. He could have biked 1 or 2 hours and still walked, but to check, we must see that for every one hour he bikes, he would cover the same distance in 3 hours of walking, as shown in ANOTHER equation, where W is Walking Distance and B is Biking Distance:
B=3W -- This means for every one distance he covers biking it takes 3 walking distance times. (It is 3 times longer to reach the same amount of distance he covers biking when he walks it)
Here's the equations we have:
W+B=36miles
Wt=Bt+1
B=3W
We know Tyrell didn't bike 3 hours, and if he biked 1 hour then the rest of the distance walking would HAVE to be 2 hours worth to follow the information given, but that doesn't work, because the total distance would also HAVE to equal 36, yet it would equal 12+4+4=20 (not 36)
Next we try 2 hours of biking (so he would have to do biking time+1 for walking to get 3 hours of walking) and this comes out to be:
24+12=36
In this situation, he follows the way of going one more hour than he bikes in walking (3 hours of walking and 2 hours of biking) and the total distance of these adds up to 36 miles. The answer is: he spent 2 hours biking and 3 hours walking
