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基本的速率問題 (英) : 基本的速率問題
- We're told that as part of an experiment about train speed,
- 4 different train conductors measured the distance that
- they covered over a certain amount of time
- during a recent journey.
- So these are the 4 trains.
- This is how long it took them to go this many miles.
- However, they all use different time intervals.
- Yeah, you see this guy, he did it over half an hour.
- This guy did it over 2 hours.
- And they're having a difficult time comparing their data.
- According to the data provided, were all 4 trains
- moving at the same speed during the experiment?
- So we just have to figure out what was the speed of all of
- these 4 trains based on how far they went in
- this amount of time.
- And just to remind us, you might already know this, but
- you know that distance is equal to rate times time.
- Or if you were to divide both sides of this equation by
- time, I could do that.
- If you divide both sides by time, the times cancel out and
- you get rate is equal to distance divided by time.
- Rate is the same thing as speed, and it makes sense that
- it's distance divided by time.
- You've heard miles per hour or meter per second or
- kilometers per hour.
- Rate speed is distance divided by time.
- So we can just use this.
- We can just divide the distance by the time for each
- of these trains and figure out what their speed was.
- So let's do that.
- So let's write their speeds.
- I'll make another column for their speed right here.
- So what's this first guy?
- He went 27.5 miles in 0.5 hours.
- So once again, let's divide the distance for this train 1.
- He went 27.5 miles in 0.5.
- So if you divide something by 0.5, this is the same thing as
- 27.5 times 2.
- Let me do it this way, times 2.
- What's 27.5 times 2?
- It is 55, and it is miles per hour.
- So his speed is 55 miles per hour.
- Now, this guy, this is pretty straightforward.
- He went 55 miles in exactly 1 hour.
- The distance divided by time is 55.
- So this guy's pretty straightforward.
- He's also 55.
- And you can put it in the formula.
- 55 is the distance.
- The time is 1 hour.
- 55 over 1.
- 55 miles per hour.
- Now this guy went 82-1/2 miles in 1-1/2 hours.
- Let's see what that is.
- So he went 82-1/2 miles in 1.5 hours.
- So let's figure out what this is.
- And I'll have to do a little bit of decimal long division
- to do this.
- So we have 1.5 goes into 82.5.
- Let's multiply both of these numbers by 10, essentially
- shift their decimals one over, so shift that
- decimal over here.
- So it becomes 15 goes into 825 how many times?
- So 15 doesn't go into 8 at all.
- It goes into 82 five times.
- 5 times 5 is 25, carry the 2.
- 5 times 1 is 5, plus 2 is 70.
- Subtract 75.
- 82 minus 75 is just a 7, right?
- And then you bring down this 5.
- 15 goes into 75 five times exactly.
- 5 times 15 is 75.
- Subtract, no remainder.
- So 82.5 miles in an hour and a half is also
- 55 miles per hour.
- And then finally, if you do 110 miles 2 hours, 110 divided
- by 2 is 55.
- So they did indeed all go, or they all did move at the same
- speed during the experiment.