a steamboat travels 9 km faster than a freighter. The steamboat travels 147 km/in the same time the freighter travels 120 km/
find the speed of each boat?
if the steamboat's speed is s, then since time=distance/speed,
147/s = 120/(s-9)
To find the speed of each boat, let's first set up some variables.
Let's say the speed of the freighter is x km/h. Since the steamboat travels 9 km/h faster than the freighter, its speed can be represented as (x + 9) km/h.
We know that the time it takes for both boats to travel their respective distances is the same.
Now, we can use the formula: speed = distance / time.
For the freighter:
Speed = x km/h
Distance = 120 km
Time = Distance / Speed = 120 / x
For the steamboat:
Speed = (x + 9) km/h
Distance = 147 km
Time = Distance / Speed = 147 / (x + 9)
Since the time it takes for both boats to travel their respective distances is the same, we can set up the equation:
120 / x = 147 / (x + 9)
To solve this equation, we can cross-multiply:
120(x + 9) = 147x
120x + 1080 = 147x
Now, let's isolate the x variable by moving the terms around:
120x - 147x = -1080
-27x = -1080
Divide both sides by -27:
x = -1080 / -27
x = 40
So the speed of the freighter is 40 km/h.
The speed of the steamboat is (x + 9) = (40 + 9) = 49 km/h.
Therefore, the speed of the freighter is 40 km/h, and the speed of the steamboat is 49 km/h.