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Algebra I Drill 2, Problem 3. Which of the following is the same as the expression?
SAT Diagnostic #2 189 Views
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Description:
SAT Diagnostic #2
Transcript
- 00:03
Algebra and functions: world problem a'la shmoop
- 00:07
Lance rode his bike to school pedaling at an average speed of 12 miles per hour. [Lance riding his bike to school]
- 00:13
When he rode his bike back home at a leisurely pace of 10 miles per hour, it took him an
- 00:18
extra 15 minutes.
- 00:20
So..how far is his school from his home?
Full Transcript
- 00:24
And here are the potential answers…
- 00:25
As you know, a full day of school can really sap your energy. [Tired boy sleeping after a exhausting day at school]
- 00:30
So it’s no surprise that Lance is draggin’ a bit on the way home.
- 00:34
This question is asking about the difference that those 2 miles an hour make… [Road leading from school to lance's home]
- 00:38
…since they lost Lance an extra 15 minutes.
- 00:41
Time that could have been well spent doing math homework. [Boy doing math homework]
- 00:44
Okay, formula time.
- 00:45
There's a basic equality here – since Lance is traveling the same distance both ways. [Lance travelling down a road from home to his school and riding back]
- 00:51
It's just taking him a little longer on the way back home.
- 00:53
Pick up the pace, boy…
- 00:56
All right…so let’s call the 12 miles per hour average Lance took to get to school “12x”…
- 01:01
…and the time it took him to get home “10x + 0.25”.
- 01:07
The 10x represents his average speed on the way home…
- 01:11
… and the “0.25” represents the extra quarter of an hour it takes him to pedal his [clock ticking by]
- 01:15
way home.
- 01:16
Because Lance is traveling an equal distance both times, we can say that 12x = 10x + 2.5.
- 01:25
Take away 10x from both sides…
- 01:28
And we get 2x = 2.5.
- 01:30
Divide both sides by 2 and we have a value for our “x”…1.25 hours. [2x and 0.25 divided by 2]
- 01:35
That’s nice and all… but we’re solving for distance. [Boy shrugging his shoulders at math equations]
- 01:40
So we still have to multiply the time by Lance’s average speed.
- 01:43
We take 1.25 hours multiplied by 12 miles per hour which gives us our final answer…15
- 01:50
miles.
- 01:51
Looks like the answer is option E – Lance has a 15 mile ride to and from school. [Lance cycles across the screen]
- 01:57
Sheesh.
- 01:58
We get tired driving our car for 15 miles… [Man falling asleep on his steering wheel]
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