One boat travels 10 km/h faster than a another. While on boat travels 120 km, the other travels 155 km. Fine their speed.
since time = distance/speed, if the slower boat's speed is x, then
120/x = 155/(x+10)
To find the speeds of the two boats, let's assign variables to their speeds.
Let's say the speed of the first boat is "x" km/h, then the speed of the second boat would be "x + 10" km/h (since it is traveling 10 km/h faster).
Now, we are given that the first boat travels 120 km and the second boat travels 155 km.
We can use the formula:
Speed = Distance / Time
For the first boat, we have:
x = 120 / Time1
For the second boat, we have:
x + 10 = 155 / Time2
Since the time taken would be the same for both boats (as they start and end at the same time), we can set Time1 equal to Time2.
So, we have:
120 / Time1 = 155 / Time2
Cross-multiplying, we get:
120 * Time2 = 155 * Time1
Now, we need to relate the speeds of the boats to time. Since Time = Distance / Speed,
we have:
Time1 = 120 / x
Time2 = 155 / (x + 10)
Substituting these values in the previous equation, we get:
120 * (155 / (x + 10)) = 155 * (120 / x)
Simplifying further, we have:
120 * 155 = 155 * (120 / x) * (x + 10)
Now, we can solve this equation to find the value of x.
By canceling out common terms, we get:
120 = (120 / x) * (x + 10)
Cross-multiplying, we have:
120x = 120 * (x + 10)
Expanding, we get:
120x = 120x + 1200
Subtracting 120x from both sides, we get:
0 = 1200
This is a contradiction, indicating that there is no solution. It means that there is no combination of boat speeds that satisfies the given conditions.