On a 60 km straight road,a bus travels the first 30km with a uniform speed of 30kmh .How fast must the bus travel the next 30 km so as to have average speed of 40 kmh for entire trip.
First 30km with a speed of 30km/h means it took 1 hour.
For an average of 40km/h over 60 km, total time = 60/40 = 1.5 hours.
Time left for 30 km = 1.5-1 = 0.5 h.
Can you calculate the speed needed for the second half of the journey?
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Total Time taken t= distance / average speed=60/40=1.5h
Time taken to cover first half T1=30/30=1h
Time taken to cover second half T2=30/V
Now,T=T1+T2=1.5=1+30/V
Then,1.5V=1V+30
30=1.5V-1V
30=0.5V
30/0.5=V
Hence,V=60kmh
To find out how fast the bus must travel the next 30 km, we need to use the concept of average speed.
Let's denote the speed at which the bus must travel for the next 30 km as "x" km/h.
We know that average speed is the total distance traveled divided by the total time taken.
The total distance traveled is 60 km (30 km for the first part, and 30 km for the next part).
The total time taken is the sum of the time taken for the first part and the time taken for the next part.
For the first part:
Time = Distance / Speed
Time = 30 km / 30 km/h
Time = 1 hour
For the next part:
Time = Distance / Speed
Time = 30 km / x km/h
Time = 30/x hours
The total time taken for the entire trip is the sum of the time taken for the first part and the time taken for the next part.
Total time = 1 hour + 30/x hours
Now, we can use the formula for average speed to set up an equation:
Average speed = Total distance / Total time
40 km/h = 60 km / (1 hour + 30/x hours)
Now, we can solve this equation to find the value of x.
Multiplying both sides of the equation by (1 hour + 30/x hours):
40 km/h * (1 hour + 30/x hours) = 60 km
Expanding:
40 km * 1 hour + 40 km * 30/x hours = 60 km
40 km + 1200 km/x = 60 km
Subtracting 40 km from both sides:
1200 km/x = 20 km
Cross-multiplying:
20 km * x = 1200 km
Dividing both sides by 20 km:
x = 60 km/h
Therefore, the bus must travel the next 30 km at a speed of 60 km/h in order to have an average speed of 40 km/h for the entire trip.