a train travels the first 30 km of 120 km track with a uniform speed of 30km/h.What should be the speed of train to cover the remaining distance of the track so that its average speed is 60km/h for the entire trip

To solve this problem, we'll use the formula for average speed:

Average Speed = Total Distance / Total Time

We know that the total distance is 120 km, and we need to find the speed for the remaining distance. Let's denote the remaining distance as D km.

First, let's find the time it takes to travel the first 30 km with a speed of 30 km/h. We can use the formula:

Time = Distance / Speed

So, the time taken to travel the first 30 km is:

Time1 = 30 km / 30 km/h = 1 hour

Now, let's find the time it takes to travel the remaining distance (D km) with an unknown speed (let's call the speed v km/h). Again, we can use the formula for time:

Time2 = D km / v km/h

Now, we know that the average speed for the entire trip is 60 km/h. So, we can write the equation for average speed:

60 km/h = (30 km + D km) / (1 hour + Time2)

Simplifying this equation:

60 km/h = (30 km + D km) / (1 + D/v) hour

Cross-multiplying:

60 km/h * (1 + D/v) hour = 30 km + D km

60 km + 60D/v km/h * hour = 30 km + D km

60D/v km/h * hour - D km = 30 km - 60 km

D (60/v - 1) km = -30 km

D (60 - v)/v km = -30 km

Now, let's solve for the remaining distance D:

D = -30 km * v / (60 - v)

Since distance cannot be negative, we'll discard the negative sign:

D = 30 km * v / (60 - v)

So, the speed of the train to cover the remaining distance should be v km/h, where v is given by:

v = D * (60 - v) / 30 km

Now, we can solve this equation to find the value of v.

Total distance = 120 km

For an average of 60km/h,
total time available = 120/60=2 hours

Distance left = 120-30=90 km
Time left = 2-1 = 1 hour

What is the speed need for the remaining distance?

avg speed= distance/totaltime

total time=time1+time2
= 30km/30km/hr + time2

avg speed=60=120/total time
total time=120/60=2h
30km/30km/hr + time2=2 hr
time2=1hr
but speed2=90km/1hr=90 km/hr

a train normally travel at a uniform speed of 24 km per hour