A boat travels from one port A to port B, travelling 126 km, upstream (against the current) at a uniform speed, and the trip takes 6 hours. On the way back (downstream), the trip only takes 4.5 hours.
Set up and solve a system of equations to find out the speed of the boat in still water and the speed of the current.
Let b = speed of boat km/h
Let c = speed of currrent in km/h
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How would I solve this? I'm having trouble setting up equations.
the distance traveled is the same: 126 km. So, since distance = speed * time,
6(b-c) = 126
4.5(b+c) = 126
Oh okay. Now I'll try to solve it and can you let me know if my answer will be right?
I got b=24.5 and c=3.5
Do you want to see my work as well?
nah - that's what I got.
Thank you so much! It's just that I have trouble making the equations. I can do it r simpler problems bit it gets difficult for me
Thank you!!!
i hat math
To solve this problem, we can use the relationship between distance, time, and speed. Let's start by setting up the equations.
1. Upstream Journey:
Distance = Speed x Time
Using the given information, the distance is 126 km, and the time taken is 6 hours. However, since the boat is traveling upstream (against the current), its effective speed will be reduced by the speed of the current. Therefore, the boat's speed relative to the ground will be (b - c) km/h (where b is the speed of the boat and c is the speed of the current). So, the equation becomes:
126 = (b - c) x 6
2. Downstream Journey:
Using the same reasoning, the distance is still 126 km, but the time taken is now 4.5 hours. Since the boat is traveling downstream (with the current), its effective speed will be increased by the speed of the current. Hence, the boat's speed relative to the ground will be (b + c) km/h. So, the equation is:
126 = (b + c) x 4.5
We now have a system of two equations with two unknowns, which we can solve simultaneously to find the values of b and c.
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:
Multiply Equation 1 by 4.5 and Equation 2 by 6 to eliminate (b - c):
567 = 27b - 27c (Equation 3)
756 = 27b + 27c (Equation 4)
Add Equation 3 and Equation 4:
567 + 756 = 27b - 27c + 27b + 27c
1323 = 54b
Now, we can solve for b:
b = 1323 / 54
Simplifying, we get:
b ≈ 24.5 km/h
To find c, substitute the value of b into either Equation 3 or Equation 4:
27b + 27c = 756
27(24.5) + 27c = 756
661.5 + 27c = 756
Now solve for c:
27c = 756 - 661.5
27c ≈ 94.5
c ≈ 3.5 km/h
Therefore, the speed of the boat in still water is approximately 24.5 km/h, and the speed of the current is approximately 3.5 km/h.