A boat can travel 16 km/h against the current.The same boat can travel 30 km/h with the current.find the rate of the boat in still water and the rate of the current.
Could someone help me.it seams like an easy problem, but I am not getting there.Thank YU very much.
speed of boat in still water ---- x km/h
speed of current ------- y km/h
x+y = 30
x-y = 16
add them
2x = 46
x = 23
then y = 7
speed in still water is 23 km/h, speed of current is 7 km/h
30
To solve this problem, let's assume that the rate of the boat in still water is represented by the variable "b," and the rate of the current is represented by the variable "c."
When the boat is traveling against the current, its effective speed is reduced. In this scenario, the boat is traveling at 16 km/h. The speed of the current is subtracted from the boat's speed to get the effective speed. Therefore, the equation becomes:
b - c = 16 ---- (Equation 1)
When the boat is traveling with the current, the current helps to increase its speed. In this scenario, the boat is traveling at 30 km/h. The speed of the current is added to the boat's speed to get the effective speed. Therefore, the equation becomes:
b + c = 30 ---- (Equation 2)
We now have a system of two equations to solve simultaneously. We can use either substitution or elimination method to solve these equations. Let's use the elimination method:
Add Equation 1 and Equation 2 together:
(b - c) + (b + c) = 16 + 30
2b = 46
b = 46/2
b = 23
Substitute the value of b into Equation 2:
23 + c = 30
c = 30 - 23
c = 7
Therefore, the rate of the boat in still water is 23 km/h, and the rate of the current is 7 km/h.
Sure, I can help you with that problem. In this problem, we need to find two unknowns - the rate of the boat in still water (let's call it "b") and the rate of the current (let's call it "c").
To solve this problem, we can use the concept of relative speed. When a boat is traveling against the current, its effective speed is reduced by the speed of the current. Similarly, when the boat is traveling with the current, its effective speed is increased by the speed of the current.
Let's analyze the given information. The boat travels at a speed of 16 km/h against the current. This means that the effective speed of the boat is 16 km/h slower than its speed in still water. Therefore, we can write the following equation:
b - c = 16 ----> Equation 1
Similarly, when the boat travels with the current, its effective speed is increased by the speed of the current. The boat travels at a speed of 30 km/h with the current. Therefore, we can write the following equation:
b + c = 30 ----> Equation 2
Now we have a system of two equations (Equation 1 and Equation 2) with two unknowns (b and c). We can solve this system of equations using different methods, such as substitution or elimination.
Let's solve it using the elimination method. We can add the two equations together to eliminate the "c" term:
(b - c) + (b + c) = 16 + 30
2b = 46
b = 23
Now, we can substitute the value of b into either Equation 1 or Equation 2 to find the value of c. Let's use Equation 1:
23 - c = 16
-c = 16 - 23
-c = -7
c = 7
Therefore, the rate of the boat in still water is 23 km/h, and the rate of the current is 7 km/h.
I hope this explanation helps you understand how to solve this type of problem!