Niles and Bob sailed at the same time for the same length of time. Niles' sailboat traveled 30 miles at a speed of 5 mph, while Bob's motorboat traveled 114 miles at a speed of 19 mph. For how long were Niles and Bob traveling?
We can use the distance formula:
distance = rate x time
Let's start with Niles' sailboat:
distance = 30 miles
rate = 5 mph
time = unknown
30 = 5t
Solving for t, we get:
t = 6 hours
Now let's do the same for Bob's motorboat:
distance = 114 miles
rate = 19 mph
time = unknown
114 = 19t
Solving for t, we get:
t = 6 hours
Since Niles and Bob traveled for the same amount of time, the answer is that they were traveling for 6 hours.