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# Comparing linear functions word problem: climb

Sal is given the formula and a table of values that represent two people climbing a wall, and is asked to determine which one started out higher. Created by Sal Khan.

## Want to join the conversation?

• it was hard i didn´t get it??
• The goal here is to find who started off higher than the other.

Finding Alyssa's height is fairly straightforward.

a=1/3t+5

We substitute "0" for "t".
a=1/3(0)+5

This removes 1/3 making:
a=5

Alyssa started off at 5 feet up the wall.

t|Nick's height
6|6
8|7
10|8

Every 2 seconds Nick goes up one foot.
Nick is moving at 1/2 a foot per second.

We divide one of the x value of 6 by 2 giving us 3.

To find Nick's height we can make an equation

Nick's height=1/2(x)+3
if x=6
Nick's height=1/2(6)+3
6/2=3
3+3=6

We have proved that b=3.

Nick's height when he started was 3 feet.
Alyssa's height when she started was 5 feet.

Alyssa started off higher than Nick.
• can't you also use y=mx+b
(1 vote)
• That is exactly what he is doing, he just substituted n for y and t for x. The variables make the problem a little bit easier to understand.
• What would Alyssa's height be?
• 5ft, he said at the beginning of the video
• Do we know the formula of the slope?
• W(t)=23t, i do not get this. really confused
(1 vote)
• W is the function of t, in this case, 23 is equal to W, if you give a input:

for example, 2, then this function would be:
W(2)=23(2)
And the output of this function would be 46

Remember, a function can only have one output. This is how I think of it, hope it helps!
(1 vote)
• Compare features of two real-world relationships that can be modeled by linear functions, where the functions are represented in different ways.
(1 vote)
• On the previouse exercise there was a question:
P(x)=-2x+10 and Q(x)=-11/5x+10 Which linear function has a greater rate of change?
The answer was P(x) since the slope -2>-11/5
But function Q(x) decreases by 11 when x increses by 5 and function P(x) decreases by 10 when x increses by 5. It is clear that Q(x) steeper than P(x) so shouldn't Q(x) has a greater rate of change than P(x)?
• No it isn't clear. smh watch the video again its right there.