how can you find avarage speed without time or distance

Question

1.You want to a trip in a time of T hours with an average speed of 60.0 km/h. After having traveled T/2 hours, you noticed that your average speed so far was 45.0 km/h. What should your average speed be for the remaining time?

Answer 1

Lets break this question down. First, remember that d = v t where d = distance, v = average velocity/speed, and t is the time.

So we can write the total distance for the trip is D = (60.0 km/hr)T

Using the same equation, we can write the distance traveled over the first T/2 hours is

D₁ = (45 km/hr) T/2 = 22.5 T (km)

Similarly the distance that needs to be covered in the second T/2 hours is

D₂ = V₂ (T/2)

We also know that the total distance traveled, D = D₁ + D₂; this can be solved for D₂,

D₂ = D - D₁ = 60 T - 22.5 T (km) = 37.5 T (km)

Substituting into the equation for D₂, gives 37.5 T = V (T/2); solve for V₂: V₂ = (2/T)(37.5 T), cancel T from numerator and denominator, V₂ = 2 (37.5) = 75 km/hr

Check the answer: (45 + 75)/2 = 60? Yes, solution is correct.