A car moves a distance of 200 km. It covers the first half of the distance at speed 40 km/h and second half of the distance by speed v. The average speed is 48 km/h. Find the value of v
Total time = 100/40 + 100/v = 200/48
100/v = 4.167 - 2.500 = 1.667 hours
v = 60 km/h
tnxx
To find the value of v, we can use the average speed formula:
Average speed = Total distance / Total time
We are given that the car moves a distance of 200 km and has an average speed of 48 km/h. Let's denote the speed of the second half of the distance as v.
The time taken to cover the first half of the distance can be calculated using the formula:
Time = Distance / Speed
For the first half of the distance, the speed is 40 km/h, so the time taken is:
Time1 = (200 km / 2) / 40 km/h
= 100 km / 40 km/h
= 2.5 hours
For the second half of the distance, the time taken can be calculated using the formula:
Time2 = (200 km / 2) / v km/h
= 100 km / v km/h
The total time taken is the sum of the time taken for the first and second halves of the distance:
Total time = Time1 + Time2
= 2.5 hours + 100 km / v km/h
Using the average speed formula, we have:
Average speed = Total distance / Total time
48 km/h = 200 km / (2.5 hours + 100 km / v km/h)
To get rid of the fractions, we can multiply both sides of the equation by (2.5 hours + 100 km / v km/h):
48 km/h * (2.5 hours + 100 km / v km/h) = 200 km
Expanding this equation gives:
120 km + 4800 km / v = 200 km
Subtracting 120 km from both sides gives:
4800 km / v = 80 km
Multiplying both sides by v gives:
4800 km = 80 km * v
Dividing both sides by 80 km gives:
v = 4800 km / 80 km
Simplifying this expression gives:
v = 60 km/h
Therefore, the value of v is 60 km/h.
To find the value of v, we can use the formula for average speed:
Average Speed = Total Distance / Total Time
We are given that the average speed is 48 km/h, and we know the total distance is 200 km. Let's denote the time taken for the first half of the distance as t1, and the time taken for the second half as t2.
Since the car covers the first half of the distance at a speed of 40 km/h, the time taken for this portion can be calculated using the formula:
t1 = Distance / Speed
t1 = 100 km / 40 km/h
t1 = 2.5 hours
For the second half of the distance, the speed is v km/h. So, the time taken for this portion can be calculated using:
t2 = Distance / Speed
t2 = 100 km / v km/h
t2 = 100/v hours
Now we can find the total time taken by adding t1 and t2:
Total Time = t1 + t2
Total Time = 2.5 hours + 100/v hours
We know that the average speed is 48 km/h, and using the formula for average speed, we have:
48 km/h = 200 km / (2.5 hours + 100/v hours)
To solve for v, we need to rearrange this equation. First, let's multiply both sides of the equation by (2.5 hours + 100/v hours) to get rid of the denominator:
48 km/h * (2.5 hours + 100/v hours) = 200 km
Now, let's simplify the equation:
120 km + 4800/v km/h = 200 km
Subtract 120 km from both sides of the equation:
4800/v km/h = 200 km - 120 km
4800/v km/h = 80 km
To isolate v, let's multiply both sides of the equation by v:
4800 km/h = 80 km * v
Divide both sides of the equation by 80 km:
v = 4800 km/h / 80 km
v = 60 km/h
Therefore, the value of v is 60 km/h.