average speed

Question

Having traveled the first 0.25 of the distance of your trip at an average speed of 20.0 km/hr, how fast must you travel for the rest of the trip in order to average 25.0 km/hr?

Answer 1

Let d be the total distance traveled.

t₁ = time taken to traverse first .25d, with average speed v₁=20km/hr

t₂= time taken to traverse remaining .75d, with average speed v₂.

trip avg=v_avg = (total distance)/(total time) = d/(t₁+t₂) 

Or v_avg* (t₁ + t₂) = d

Or 25(.25d/20 + .75d/v₂) = d

Or 25(.25 + 15/v₂) = 20 [ multiply by 20/d on both sides]

6.25 + 375/v₂ = 20

Or 375/v₂= 13.75

Or v_{2 = 375/13.75 =27.27}

He must travel rest of the journey at 27.27 km/hr