a boat took 5 hours to travel 60 km up a river, against the current. the return trip took 3 hours. find the speed of the boat in still water and the speed of the current.
if possible, show your steps
speed of boat in still water ---- x km/h
speed of current ---- y km/h
effective speed with the current = x+y km/h
effective speed against the current = x-y km/h
time to go 60 km against the current = 60/(x-y) hours = 5
5x - 5y = 60 or x - y = 12
time to go 60 km with the current = 60/(x+y) = 3
3x + 3y = 60 or x + y = 20
solve for x and y, (add the two equation to start)
time to go 60 km with the current = 60/(x-y) hours
60/(x+y) + 60/(x-y) =
Let's assume the speed of the boat in still water as "B" and the speed of the current as "C." We need to find the values of B and C.
We know that the boat took 5 hours to travel 60 km up the river against the current, and 3 hours for the return trip.
To find the speed of the boat in still water, we can establish the following equation:
60 km = (B - C) * 5
Similarly, to find the speed of the boat in still water for the return trip, we can establish another equation:
60 km = (B + C) * 3
Now, let's solve these equations to find the values of B and C.
From the first equation:
60 km / 5 = B - C
12 = B - C ------ (equation 1)
From the second equation:
60 km / 3 = B + C
20 = B + C ------ (equation 2)
We now have a system of equations (equation 1 and 2) that we can solve simultaneously to find the values of B and C.
Adding equation 1 and equation 2 together, we get:
12 + 20 = (B - C) + (B + C)
32 = 2B
B = 16
Now, substitute the value of B into equation 2 to find the value of C:
20 = 16 + C
C = 20 - 16
C = 4
Therefore, the speed of the boat in still water is 16 km/h, and the speed of the current is 4 km/h.
To find the speed of the boat in still water (let's call it "b") and the speed of the current (let's call it "c"), we can use the following information:
1. The boat took 5 hours to travel 60 km up the river, against the current.
2. The return trip (going with the current) took 3 hours.
Let's start by using the formula:
Speed = Distance / Time
For the boat going up the river (against the current), the effective speed is reduced by the speed of the current. So we can write the equation:
b - c = 60 / 5
Simplifying this equation, we get:
b - c = 12
For the return trip (going with the current), the effective speed is increased by the speed of the current. So we can write the equation:
b + c = 60 / 3
Simplifying this equation, we get:
b + c = 20
Now we have a system of equations with two variables (b and c):
b - c = 12
b + c = 20
To solve this system, we can add the two equations together:
(b - c) + (b + c) = 12 + 20
This simplifies to:
2b = 32
Dividing both sides by 2:
b = 16
Now we can substitute this value back into one of the original equations to find the speed of the current. Let's use the second equation:
16 + c = 20
Subtracting 16 from both sides:
c = 4
Therefore, the speed of the boat in still water is 16 km/h, and the speed of the current is 4 km/h.
Eq1: Vb - Vc = 60/5 = 12km/hr,
Eq2: Vb + Vc = 60/3 = 20 km/hr,
Add Eq1 and Eq2:
Vb - Vc = 12,
Vb + Vc = 20,
sum: 2Vb = 32,
Vb = 16 km/hr = Speed of the boat in still water,
Vb + Vc = 20,
16 + Vc = 20,
Vc = ?.