Question

Niles and Bob sailed at the same time for the same length of time. Niles' sailboat traveled 36 miles at a speed of 6 mph, while Bob's motorboat traveled 96 miles at a speed of 16 mph. For how long were Niles and Bob traveling?

Answer 1

Niles and Bob were traveling for 6 hours.

Explanation:

The speed or rate at which an object is moving can be computed using the formula:

`s=(d)/(t)`

Here:

s = speed

d = distance traveled

t = time taken

It is provided that Niles and Bob sailed at the same time for the same length of time.

Speed of Niles sailboat is, s₁ = 6 mph.

Distance traveled by Niles' sailboat is, d₁ = 36 miles.

Speed of Bob's sailboat is, s₂ = 16 mph.

Distance traveled by Bob's sailboat is, d₂ = 96 miles.

It took both Niles and Bob the same time to travel the respective distance.

Compute the time it took Niles to travel 36 miles at 6 mph speed as follows:

`t_(1)=(d_(1))/(s_(1))`

`=(36)/(6)\\=6`

It took Niles 6 hours to travel 36 miles at 6 mph speed.

Compute the time it took Bob to travel 96 miles at 16 mph speed as follows:

`t_(2)=(d_(2))/(s_(2))`

`=(96)/(16)\\=6`

It took Bob 6 hours to travel 96 miles at 16 mph speed.

Thus, Niles and Bob were traveling for 6 hours.