Her average rate traveling uphill was 1.8 kilometers per hour and her average rate down hill was 4.2 kilometers per hour. If she spent a total of 16 hours hiking, how long was the trail?

add up the times to hike d km:

d/1.8 + d/4.2 = 16
0.5555d + .2381d = 16
d = 16/.7936 = 20.16 km

To find the length of the trail, we can use the formula:

Distance = Rate × Time

Let's assume that the time taken to travel uphill is "x" hours.

Given that the average rate traveling uphill is 1.8 kilometers per hour, we can calculate the distance traveled uphill as:
Distance uphill = Rate uphill × Time uphill
Distance uphill = 1.8 km/h × x h = 1.8x km

Since the average rate traveling downhill is 4.2 kilometers per hour, the time taken to travel downhill would be (16 - x) hours.
So, the distance traveled downhill is:
Distance downhill = Rate downhill × Time downhill
Distance downhill = 4.2 km/h × (16 - x) h = 4.2(16 - x) km

The total distance of the trail is the sum of the distance traveled uphill and downhill.
So, the length of the trail is:
Length of trail = Distance uphill + Distance downhill
Length of trail = 1.8x + 4.2(16 - x) km

To find the value of "x" and calculate the length of the trail, we can solve the equation:
1.8x + 4.2(16 - x) = Length of trail

Now we can proceed to solve the equation to find the length of the trail.