A car completes a journey in 10 minutes. For the first of the distance the speed was 60 km/h and for the second half the speed was 40 km/h. how far is the journey?
Let the total distance be x.
(x/2)/60 + (x/2)/40 = (10minutes)/(60minutes/hour)
x/120+x/80 = 1/6
multiply by common denominator 240
2x+3x = 40
5x=40
x=8 km
To find the distance of the journey, we can use the formula:
Distance = Speed × Time
Let's break down the journey into two parts:
First part: The car traveled at a speed of 60 km/h for a certain distance.
Second part: The car traveled at a speed of 40 km/h for the remaining distance.
Given that the car completed the journey in 10 minutes, which is equivalent to (10/60) hours, we can calculate the time spent on each part:
First part time = 10/60 × 1/2 = 1/12 hours
Second part time = 10/60 × 1/2 = 1/12 hours
Now, we can calculate the distance of each part:
First part distance = 60 km/h × 1/12 hours = 5 km
Second part distance = 40 km/h × 1/12 hours = 1/3 km
Finally, we can find the total distance by adding the distances of both parts:
Total distance = First part distance + Second part distance
= 5 km + 1/3 km
= 15/3 km + 1/3 km
= 16/3 km
Therefore, the total distance of the journey is 16/3 km.
To find the distance of the journey, we can use the formula Distance = Speed × Time. Since the car completed the journey in two different speeds, we need to calculate the distance for each half of the journey separately.
Let's start with the first half of the journey, where the speed was 60 km/h. We need to figure out the time it took for the car to cover this distance. To do that, we can rearrange the formula to Time = Distance ÷ Speed.
Since we don't know the distance yet, let's call it 'd' for now. The time taken for the first half of the journey is 10 minutes, which can be converted to hours by dividing by 60 (since there are 60 minutes in an hour): 10 minutes ÷ 60 = 1/6 hour.
Plugging these values into the formula, we have 1/6 hour = d ÷ 60 km/h. Rearranging this equation, we find that d = 1/6 hour × 60 km/h = 10 km.
Now, let's move on to the second half of the journey, where the speed was 40 km/h. We use the same formula, Time = Distance ÷ Speed, but this time the time is 10 minutes as well, or 1/6 hour.
Using the same approach as before, we find that the distance for the second half is also 10 km.
Finally, to find the total distance of the journey, we add the distances for the first and second halves: 10 km + 10 km = 20 km.
Therefore, the total distance for the journey is 20 kilometers.