A train travel some distance with a speed of 30km/hr and return with a speed of 45km/hr. Calculate average speed.
let d/2 be the distance covered by train with a speed of 30kmph in t1 hours
→t1=d/60
it covers d/2 distance with a speed of 45km/h in t2 hours
→t2=d/90
average speed = total distance/total time
=d/(t1+t2)
=1/(1/60+1/90)
=1/(3+2)/180
=180/5=36kmph
To calculate average speed, we need to consider the total distance traveled and the total time taken.
Let's assume the distance traveled in one direction is 'd' kilometers.
The time taken to travel the distance 'd' at a speed of 30 km/hr can be calculated using the formula: time = distance/speed = d/30.
Similarly, the time taken to return the same distance 'd' at a speed of 45 km/hr can be calculated using the formula: time = distance/speed = d/45.
Now, to find the total time taken for the round trip, we can add the time taken in both directions: total time = d/30 + d/45.
To calculate the average speed, we need to use the formula: average speed = total distance/total time.
In this case, the total distance can be calculated by adding the distance traveled in both directions: total distance = d + d = 2d.
So, the average speed = total distance/total time = 2d/(d/30 + d/45).
Now, we can simplify this expression to calculate the average speed.
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Average speed =
=Total distance/ total time =
= 2s/{t₁ +t₂} =
= 2s/{s/v₁) +(s/v₂)} =
=2v₁v₂/(v₁+v₂) =
=2•30•45/(30+45) = 36 km/h