Please Answer this with work included?

Question

You plan a trip on which you want to average 90km/h. You cover the first half of the distance at an average speed of only 48km/h. What must your average speed be in the second half of the trip to meet your goal? Note that the velocities are based on half the distance, not half the time.

Answer 1

time to complete journey: d/v (v is target time)

time you took to complete first leg: d / 2 v1

time remaining: d/v - d / 2v1

distance remaining: d/2

velocity required = distance remaining / time remaining
= d/2 / (d/v - d / 2 v1)
= v1 v / (2v1 - v)

They give you v1 and v. Plugnchug.

EDIT--You didn't mess up Flood. 720 is the answer. Look at it this way, if you want to average 90 and you finish the first have at a speed of 45, you have no time left and need to finish with infinite speed. So if the first half was at 48, you're still just about out of time and have to go damn fast.

Answer 2

Let d be the distance (in km). The the time t (in hours) it takes to cover d at 90 km/h is d/90. If you went half the distance at 48 km/hr it took you (d/2)/48 = d/96 hours. The speed (s) you need to average d/90 must then be
d/96 + (d/2)/s = d/90 or d/96 + d/2s = d/90
Now it's just a bit of algebra and you're home free ☺

Doug

Answer 3

You want to say 132km/hr but it's not.

Just say it's 100 km to go there.

If you went that far it would be 100km / 48km/hr

2.08333 hours

Now the average velocity needs to be 90km/hr

Average velocity x time = Distance

Time = Distance / Average velocity

Time = 200km / 90km/hr

Time = 2.22222 hours

So you need to go 100 more km in 0.1389 hours.

That's 719.94km/hr!!!

I messed up somewhere.