since time = distance/speed,
350/x = (470-350)/(x-15)
350/x = (470-350)/(x-15)
(x-15) be the average speed during other part of the journey.
Time Taken for 1st Part of Journey = 350 / x = 350/x hrs and
Time Taken for the 2nd part = (470-350) / (x-15) = 120 / (x-15) hrs
Since time taken for both the journeys, therefore,
350 / x = 120 / (x-15)
350(x-15) = 120x
350x-5250 = 120x
350x-120x = 5250
230x = 5250
x = 5250/230
x = 525/23 = 22.83 km/hrs approx. be the average speed for 1st journey thus x-15 = 22.83-15 = 7.83 km/hr is the average speed for the 2nd journey and hence this is the answer.
Speed = Distance / Time
Let's assume the average speed for the first part of the journey is "x" km/h.
We know that Kate cycles the first 350 km of the journey at an average speed of "x" km/h. So, the time taken to travel this distance is:
Time taken = Distance / Speed
Time taken = 350 km / x km/h
For the second part of the journey, we know that the average speed is 15 km/h less than the first part of the journey. So, the average speed for the second part of the journey is (x - 15) km/h.
The distance for the second part is the remaining distance after completing the first part of the journey, which is:
Remaining distance = Total distance - Distance of the first part
Remaining distance = 470 km - 350 km
Remaining distance = 120 km
Now, we can calculate the time taken for the second part of the journey:
Time taken = Distance / Speed
Time taken = 120 km / (x - 15) km/h
Since the time taken for both parts of the journey is the same, we can set up an equation and solve for "x":
350 km / x km/h = 120 km / (x - 15) km/h
Cross-multiplying the equation gives us:
350(x - 15) = 120x
Expanding the equation:
350x - 5250 = 120x
Rearranging the equation:
350x - 120x = 5250
Combining like terms:
230x = 5250
Dividing both sides by 230:
x = 5250 / 230
x ≈ 22.83
Therefore, the average speed for the first part of Kate's journey is approximately 22.83 km/h.
To find the average speed for the second part of the journey, we subtract 15 from the average speed for the first part:
Average speed for the second part = 22.83 km/h - 15 km/h
Average speed for the second part ≈ 7.83 km/h
So, the average speed for the second part of Kate's journey is approximately 7.83 km/h.