What must your average speed be in the second half of the trip to meet your goal?

Question

Wee bit of help please.. =D I suck at Physics. MY answer was 126+46=172/2=86, but its WRONG! WHY?!

You plan a car trip on which you want to average 86 km/h. You cover the first half of the distance at an average speed of only 46 km/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

Okay, for simplicity's sake, let's pretend that the distance for the journey is 86km (it doesn't actually matter how far it is). So, in order to complete the ENTIRE journey at the required average speed, you need to cover the distance in ONE HOUR. At 46km/h, you cover 43km (half the distance to the finish line). It will have taken you 43/46 hours to do this. ~ 0.935 hours. So, you have 0.065 hours in which to complete the remaining 43km. Therefore you need to travel at a speed of 43/0.065km/h = ~661.5km/h.

QED

Answer 2

This is sort of a tricky question, because when most people hear the word "average," they think they're supposed to add two numbers together (such as two speed values) and then divide by two. But that is not how "average speed" is defined. Think of the true definition of average speed. It is:

(total distance)/(total time)

So, the problem says you want to make the average speed equal 86 for the whole trip. This means:

86 = (avg . speed) = (total distance)/(total time)

Now, you could solve the problem without ever knowing the total distance or total time, but it's easier to work on it if you make up a number and work with that. So, let's pretend the total distance is 86 km. That would mean the total time should be 1 hour.

Okay, now the problem says that you have driven one half of the total distance (that is, 43 km. in our example), at an average speed of 46 km/h. Again using the definition of average speed:

46 km/h = 43 km / (time for 1st half)

Now, we don't know how much (time for 1st half) is, but we can figure it out by rearranging that equation:

(time for 1st half) = 43km / (46 km/h) = 43/46 hour.

This is about 56 minutes. Yikes! You see the problem here. In our example, we wanted to cover the entire 86 km in an hour--but we've already used up almost the whole hour, and we're only halfway there! We'll have to move like a bat out of h*ll to make up the difference. We have to cover the remaining 43 km in a mere 4 minutes (more precisely, 3/46 of an hour). That means our average speed during the 2nd half of the trip will have to be:

(distance for 2nd half) / (time for 2nd half) = 43 km / (3/43 hr) = 659.3 km/h

Somehow, I don't think we'll make it. :-)

Answer 3

Say distance to shuttle is 2x, time taken is 2t, so 2x/2t = x/t = 87 yet you have travelled x already at 40 5 km/h taking time t1 t1 = x/40 5 you have time t2 left on the grounds that t1 + t2 = 2t so t2 = 2t - x/40 5 yet x = 87.t from above so t2 = ninety.t/40 5 - 87.t/40 5 = 3.t/40 5 in this final time you're able to shuttle x so your velocity ( = x/t2) for the 2nd a million/2 is: (x.40 5)/(3.t) yet x/t = 87 so that's (40 5.87)/3 = 1305 km/h

Answer 4

Let S be the full distance.

Half of it is S/2.

The average speed during the first half is U = S/ (2t’). ---------------------1
t’ is the time for the first half of the journey.

The average speed during the second half is V = S/ (2t”) --------------------2
t” is the time for second half of the journey.

The average speed for the whole journey is W = S/ ( t’ + t”) ---------------------3
( t’ + t”) is the time for the whole journey.


From 1, t’ = S/ (2U)
From 2, t” = S/ (2V)
From 3, t’ + t” = S/ (W) = S/ (2U) + S/ (2V)

1/W = ½ (1/U + 1/V)


2/W = (1/U + 1/V)

1/V = 2/W – 1/U

1/V = 2/86 – 1/ 46
1/V = 0.00152
V =659.3 km/h

Answer 5

your average speed for the second half must be 176km/h
this is true because 86/46=2.047619 that number times 86=~176 so 176=answer!=)