need to find the speed of the boat when it's going upstream and downstream

Question

speedboat can travel 32 mph in still water. It travels 150 miles upstream against the current to its starting location. The total trip time is 10 hours. What is the boats speed going upstream? 

Answer 1

Marco,

 

Let c be the speed of the current. The speed of the boat going upstream (against the current) is 32 − c and its speed going downstream (with the current) is 32 + c.

 

Remember that distance = rate × time. The distance is 150 both upstream and downstream. Solving for the time in each trip, you will have:

 

time going upstream is 150/(32 − c)

time going downstream is 150/(32 + c)

 

When you add these together, you get the total trip time, 10 hours.

 

This creates an equation

 

150/(32 − c) + 150/(32 + c) = 10.

 

The question is asking for 32 − c, so you must solve this for c and then find 32 − c.

 

To solve for c, you must clear fractions by multiplying by the LCD = (32 − c)(32 + c) on both sides of the equation.

 

After canceling the denominators, you will have

 

150(32 + c) + 150(32 − c) = 10(32 − c)(32 + c)

 

Multiply out:

 

4800 + 150c + 4800 − 150c = 10240 − 10c²

 

Collect like terms:

 

9600 = 10240 - 10c²

 

Isolate the c² term on one side:

 

10c² = 640

 

Solve for c:

 

c² = 64

 

c = √64 = 8.

 

This shows the speed of the current to be 8 mph. the speed of the boat upstream will be 32 - 8 = 24 mph. If you verify this in the statement of the original problem, you will see that it checks out.