I'LL MARK YOU BRAINLIEST IF YOU ANSWER THIS WITH RIGHT STEPS AND CLEAR EXPLANATION BECAUSE THIS IS DUE IN 10 MIN THANKS!!! In the morning, Jasmine biked to her grandma's house in 45 minutes. When she was biking back home in the evening it was foggy and she went 4 mph slower. The trip back took her 1 hour and 10 minutes. How far from her house does her grandmother live?

Here we need to solve a system of equations, we will find that the grandma's house is at 8.396 miles.

We need to remember the relation:

speed*time = distance.

First we know that Jasmine goes to her grandma's house at a speed S, and it takes 45 minutes (or 0.75 hours) to get there, so we can write:

S*0.75h = D

Where D is the distance to her grandma's house.

Returning back, she takes 1 hour and 10 minutes (or 1.167 hours) and 4 mi/h slower, then in this case her speed is:

(S - 4 mi/h)

And we can write the equation:

(S - 4mi/h)*1.167h = D

Then we have a system of equations:

S*0.75h = D

(S - 4mi/h)*1.167h = D

To solve this, we can first isolate S (because we want to solve it for D) so we have:

S = D/(0.75h)

Now we can replace this in the other equation to get:

( D/(0.75h) - 4mi/h)*1.167h = D

Now we can solve this equation for D.

D*(1.167h/0.75h) - 4mi/h*1.167h = D

D*((1.167h/0.75h) - 1) = 4mi/h*1.167h

D*0.556 = 4.668

D =  4.668/0.556 = 8.396 mi

This means that she lives at 8.396 miles from her grandmother's house.

If you want to learn more about systems of equations, you can read:

link

8.4 miles

Step-by-step explanation:

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