If a hiker walks trail B (1 mile in length) at 6 mph and trail C (3 mils in length) at 2 mph, what is the hiker's overall average speed, in mph, for hiking on the two trails?

time for trail B = 1/6 hrs

time for trail C = 3/2 hrs

total time = 1/6 + 3/2 = 5/3 hrs

avg speed = total distance / total time
= 4/(5/3) = 4(3/5) = 12/5 mph or 2.4 mph

To find the overall average speed of the hiker, we need to calculate the total distance traveled and the total time taken. We can then divide the total distance by the total time to get the average speed.

Let's calculate the time taken on each trail first:

On trail B:
Distance = 1 mile
Speed = 6 mph

Time taken on trail B = Distance / Speed
Time taken on trail B = 1 mile / 6 mph = 1/6 hour

On trail C:
Distance = 3 miles
Speed = 2 mph

Time taken on trail C = Distance / Speed
Time taken on trail C = 3 miles / 2 mph = 3/2 hour = 1.5 hours

Now, let's calculate the total distance and total time:

Total distance = distance on trail B + distance on trail C
Total distance = 1 mile + 3 miles = 4 miles

Total time = time taken on trail B + time taken on trail C
Total time = 1/6 hour + 1.5 hours = 1.6667 hours (rounded to four decimal places)

Finally, we can calculate the overall average speed:

Overall average speed = Total distance / Total time
Overall average speed = 4 miles / 1.6667 hours = 2.4 mph (rounded to one decimal place)

Therefore, the hiker's overall average speed for hiking on the two trails is 2.4 mph.