A motorist does the first part of the journey at an average speed of 54 km/h. He then increases his speed to 60 km/h for the rest of the journey. if he travels 225 km in 4 hours, what is the distance traveled for the first part of his journey????
time at slower speed --- x hrs
time at faster speed ---- 4-x hrs
54x + 60(4-x) = 225
solve for x, then evaluate 54x to find distance at slower speed
a motorist travels regularly between two towns 5 hours when tralling at a certain speed. he finds that if he increases his average speed by 15 km/h the journey take 1 hour less find his usual speed
Let's break down the information given:
- The motorist travels a total distance of 225 km.
- It takes him 4 hours to complete the entire journey.
- He increases his speed from 54 km/h to 60 km/h at some point during the journey.
To find the distance traveled for the first part of his journey, we need to determine the time taken for the first part.
Let's assume that t represents the time taken for the first part of the journey.
Since distance is equal to speed multiplied by time:
Distance for the first part = Speed for the first part × Time for the first part
We know that the speed for the first part is 54 km/h, and the total time taken for the journey is 4 hours.
So, we can set up an equation:
Distance for the first part = 54 km/h × t
Now, let's find the time taken for the first part using the total time and the time taken for the second part.
The time taken for the second part of the journey can be calculated as:
Time for the second part = Total time - Time for the first part
Time for the second part = 4 hours - t
The speed for the second part is 60 km/h, and the distance for the second part is the total distance minus the distance for the first part.
Distance for the second part = Total distance - Distance for the first part
225 km - Distance for the first part
Since the distance is equal to the speed multiplied by the time:
Distance for the second part = 60 km/h × (4 hours - t)
Now, we can equate the distances for both parts and solve for t:
54 km/h × t = 60 km/h × (4 hours - t)
54t = 240 - 60t
114t = 240
t = 240 / 114
t ≈ 2.1053 hours (rounded to 4 decimal places)
Finally, we can calculate the distance traveled for the first part:
Distance for the first part = 54 km/h × 2.1053 hours
Distance for the first part ≈ 113.736 km (rounded to 3 decimal places)
Therefore, the motorist traveled approximately 113.736 km for the first part of his journey.
To find the distance traveled for the first part of the journey, we need to determine the time it took to travel at the first speed.
Let's assume the distance traveled at the first speed is "x" km. Therefore, the distance traveled at the second speed would be (225 - x) km.
We know the average speed for the entire journey is 54 km/h, and the total time taken is 4 hours.
Using the formula speed = distance / time, we can set up the following equations:
x / 54 + (225 - x) / 60 = 4
To solve this equation, we need to isolate "x" and then solve for it.
First, we multiply the entire equation by the least common multiple (LCM) of 54 and 60, which is 540:
(540 * x) / 54 + (540 * (225 - x)) / 60 = 540 * 4
Simplifying this equation yields:
10x + 9(225 - x) = 2160
Next, distribute and consolidate like terms:
10x + 2025 - 9x = 2160
x + 2025 = 2160
Subtract 2025 from both sides:
x = 2160 - 2025
x = 135
Therefore, the distance traveled for the first part of the journey is 135 km.