Question

the average rate of the first part of yis walk on a park loop was 4 miles per hour. she then m up with a friend and the two walked the rest of the way at an average rate of 5 miles per hour. the entire 3-mile walk took yi 42 minutes (0.7 hour). which equation can be used to solve for x, the time in hours that yi spent walking before meeting her friend?

	rate (mi/h)	time (h)	distance (miles)
part 2	5	0.7 - x	5(0.7 - x)

options:
$x + (0.7 - x) = 1$
$x = 0.7 - x$
$4x + 5(0.7 - x) = 1$
$4x + 5(0.7 - x) = 3$

Explanation:

Step1: Recall distance formula

Distance = Rate × Time. For Part 1, distance is \(4x\) (rate 4, time \(x\)). For Part 2, distance is \(5(0.7 - x)\) (rate 5, time \(0.7 - x\)).

Step2: Total distance equation

Total distance of the walk is 3 miles. So sum of Part 1 and Part 2 distances equals 3: \(4x + 5(0.7 - x)=3\).

Answer:

\(4x + 5(0.7 - x) = 3\) (the fourth option, as per the given choices where the last equation is \(4x + 5(0.7 - x)=3\))