During a training exercise, a submarine travels 16 km/h on the surface and 10 km/h underwater. if the submarine traveled a distance of 160km in 12.5h, how long was it underwater?

Well, it seems like this submarine is having quite the adventure! Let's dive into the problem, shall we?

We know that the submarine travels at 16 km/h on the surface and 10 km/h underwater. If it traveled a total distance of 160 km in 12.5 hours, we can use this information to figure out how long it spent underwater.

First, let's find out how long it took for the submarine to travel 160 km on the surface. Since it travels at 16 km/h, we can divide 160 km by 16 km/h to get 10 hours. So, the submarine spent 10 hours traveling on the surface.

Now that we know this, we can subtract the time spent on the surface (10 hours) from the total time (12.5 hours) to find out how long it was underwater. So, 12.5 hours - 10 hours = 2.5 hours.

Therefore, the submarine was underwater for approximately 2.5 hours. Just enough time to spot some underwater jokes!

Let's denote the time spent on the surface as "t" and the time spent underwater as "u".

Given:
Surface speed = 16 km/h
Underwater speed = 10 km/h
Total distance traveled = 160 km
Total time taken = 12.5 hours

We can set up two equations based on the distance traveled and the time spent:

Equation 1: Distance traveled on the surface + Distance traveled underwater = Total distance
16t + 10u = 160

Equation 2: Total time taken = Time spent on the surface + Time spent underwater
t + u = 12.5

To solve these equations, we can use the method of substitution.

Let's solve Equation 2 for "t" and substitute it into Equation 1:

t = 12.5 - u

16(12.5 - u) + 10u = 160
200 - 16u + 10u = 160
-6u = -40
u = 40/6
u = 6.67

So, the submarine was underwater for approximately 6.67 hours.

To determine how long the submarine was underwater, we can use the information given about its speed on the surface and underwater.

Let's assume that the submarine spent x hours underwater.

When the submarine is on the surface, it travels at a speed of 16 km/h. So, the distance traveled on the surface can be calculated by multiplying the speed by the time spent on the surface, which is (12.5 - x) hours.

On the other hand, when the submarine is underwater, it travels at a speed of 10 km/h. So, the distance traveled underwater can be calculated by multiplying the speed by the time spent underwater, which is x hours.

The total distance traveled by the submarine is given as 160 km. Therefore, we can set up the following equation:

Distance traveled on the surface + Distance traveled underwater = Total distance

(16 km/h) * (12.5 - x hours) + (10 km/h) * (x hours) = 160 km

Now, we can solve this equation to find the value of x, which represents the time spent underwater.

16(12.5 - x) + 10x = 160

200 - 16x + 10x = 160

-6x = -40

x = 6.67 hours

Therefore, the submarine was underwater for approximately 6.67 hours.

s + u = 12.5

16s + 10u = 160