Kate cycles the first 350 km of a 470 km journey at a certain average speed and the remaining distance at an average speed that is 15 km/h less than that for the first part of the journey. If the time taken for her to travel each part of her journey is the same, find the average speed for the second part of her journey.
Let "x" be the average speed during 1st part of the journey, thus,
(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.
since time = distance/speed,
350/x = (470-350)/(x-15)
To solve this problem, we will use the formula:
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.