Question

What was the hiker's average velocity during part A of the hike?

Answer 1

@whpalmer4 I think its 5.0km/h/ north

Answer 2

what are the units for the time? minutes:seconds, or hours:minutes?

Answer 3

hours

Answer 4

Okay, so if the start time is 1:00 and the end time is 1:30, how much time passes between them?

Answer 5

30 minutes?

Answer 6

That's what I think, too :-)

So if you walk 5 km in 30 minutes, what is your average speed?

Answer 7

\[d = r * t\]\[r = \frac{d}{t}\]where \(d\) is distance, \(r\) is rate or speed, \(t\) is time

Answer 8

so 5km=r*30?

Answer 9

well, yes, but it's possible we want to talk in terms of km/hr rather than km/min when talking hiking speeds

Answer 10

so r=5km/30

Answer 11

well, we need a unit on that 30, for starters. and if we are talking about hours, it isn't 30 hours, it's 0.5 hours because there are 60 minutes in an hour

Answer 12

oh duh so r=5/0.5?

Answer 13

yes, but it is important to keep those units!
\[r = \frac{5 \text{ km}}{0.5 \text{ hour}}=\]

Answer 14

what do you get for the numeric part of that?

Answer 15

I got 10

Answer 16

Right. so the speed of the hiker is \(10 \text{ km/hr}\). To make that a velocity, we need to add a direction, which I think you've already suggested is N.

Answer 17

so 10km/0.5hrs.

Answer 18

No! 5 km/0.5 hrs = 10 km/1 hr or 10 km/hr. he went 5 km in 0.5 hrs, so the rate is 5 km/ 0.5 hr = 10 km/hr. Do you see how I went from one to the other?

Answer 19

oh yeah I do.

Answer 20

It's like saying

if you do 3 problems in 30 minutes, how many problems do you do in an hour? how many problems per hour can you do?

Answer 21

so are we agreed that 10 km/hr is the speed of the hiker? (realistically, I'm not — he'd have to be jogging to do that! :-)

Answer 22

I got 0.16666

Answer 23

where did you get that? and what is the unit?

Answer 24

well 10km/1hr.

Answer 25

Yes, 10 km/hr is the rate. But how do you get 0.16666? Oh, you're dividing 10 km by 60 minutes, right?

Answer 26

yes

Answer 27

Yeah, there's no reason to do that, unless you are looking to express the speed in km/minute.

Answer 28

oh ok thanks! :)

Answer 29

So 10 km/hr N would be the velocity

Answer 30

barring some hidden instruction to use a different set of units

Answer 31

So to find the rate, you just divide the number done by the time it took. Drive 300 miles in 6 hours, rate is 300 miles / 6 hours = 50 miles/hour. Dig 27 holes in your back yard in 9 hours, rate is 27 holes /9 hours = 3 holes/hour.

Answer 32

Lots of story problems can be solved most conveniently by finding the rates involved.

For example: you've got a swimming pool you're trying to fill up. With your garden hose running into the pool, it will take 4 hours. With your neighbor's super-thick garden hose running into the pool instead, it would take 2 hours. How long does it take to fill up if you use both hoses at the same time?

Filling with your hose, the rate is 1/4 of a pool per hour. Filling with the neighbor's hose, the rate is 1/2 of a pool per hour. Together, they fill 1/4 + 1/2 = 3/4 of a pool per hour, so to fill the entire pool takes 1 pool / (3/4 pool/hour) = 4/3 of an hour or 1 hour 20 minutes.

Answer 33

ok thanks!