Solve
One boat travels 10km/h faster than another. Which one boat travels 120 km, the other travels 155 km. Find their speeds.
rate of slow boat -- x km/h
rate of fast boat --- x+10 km/h
Your questions suggests they travelled the same time
120/x = 155/(x+10)
solve for x
To solve this problem, let's assume the speed of the slower boat is "x" km/h. Since the other boat is traveling 10 km/h faster, its speed will be "x + 10" km/h.
Now, we can use the formula:
Speed = Distance / Time
For the slower boat:
Speed of the slower boat = Distance / Time
x km/h = 120 km / t1
For the faster boat:
Speed of the faster boat = Distance / Time
(x + 10) km/h = 155 km / t2
Since both boats are traveling the same distance, we can set up the equation:
120 / t1 = 155 / t2
To simplify the equation, we can cross-multiply:
120 * t2 = 155 * t1
Now, let's solve for either t1 or t2, as both equations are equivalent.
t1 = (120 * t2) / 155
Now that we have an expression for t1, we can substitute it into the equation for the slower boat's speed:
x km/h = 120 km / ((120 * t2) / 155)
Simplifying further:
x km/h = (120 * 155) / (120 * t2)
x km/h = 18600 / (120 * t2)
x km/h = 155 / t2
Now, let's set both expressions for the speed of the slower boat equal to each other:
155 / t2 = 155 / t2
Simplifying further, we get:
155t2 = 155t2
Therefore, we can conclude that the slower boat's speed is equal to the faster boat's speed, which is 155 km/h.
To find the speed of the slower boat, we can substitute this value into the equation:
x km/h = 155 / t2
Since the slower boat travels a distance of 120 km, we can substitute that into the equation:
x km/h = 155 / (120 / t2)
x km/h = (155t2) / 120
Now, we need to solve for t2. Re-arranging the equation:
t2 = (120 * x) / 155
So, the speed of the slower boat is given by the equation:
x km/h = (155t2) / 120
Substituting the expression for t2:
x km/h = 155 * [(120 * x) / 155] / 120
Simplifying:
x km/h = (120 * x) / 120
x km/h = x
Therefore, the speed of the slower boat is x km/h.
To summarize, the speed of both boats is 155 km/h.