Question

mia and aubrey started kayaking the crow creek river at the same time. mia started at the top of the river and traveled downstream at a speed of 6 miles per hour. aubrey started 4 miles farther down the river and traveled downstream at a speed of 3 miles per hour. if they each kept a constant speed, which equation can you use to find h, the number of hours it took for mia to pass aubrey? 6h = 3h + 4 6h = 4h + 3 how long did it take for mia to pass aubrey? simplify any fractions. hours

Explanation:

First Sub - Question (Choosing the Equation)

Step1: Recall the distance formula

The distance formula is \(d = vt\), where \(d\) is distance, \(v\) is velocity (speed), and \(t\) is time. For Mia, her speed \(v = 6\) mph and time is \(h\) hours, so her distance \(d_{Mia}=6h\).

Step2: Calculate Aubrey's distance

Aubrey's speed \(v = 3\) mph and time is \(h\) hours, but she started 4 miles farther down the river. So her distance \(d_{Aubrey}=3h + 4\).

Step3: Set distances equal

When Mia passes Aubrey, their distances are equal. So \(6h=3h + 4\).

Step1: Start with the equation

We have the equation \(6h=3h + 4\).

Step2: Subtract \(3h\) from both sides

Subtracting \(3h\) from both sides gives \(6h-3h=3h + 4-3h\), which simplifies to \(3h = 4\).

Step3: Solve for \(h\)

Divide both sides by 3: \(h=\frac{4}{3}\).

Answer:

\(6h = 3h+4\)

Second Sub - Question (Finding the Time)