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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.

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• 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.
• What would Alyssa's height be?
• 5ft, he said at the beginning of the video
• 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.
• i'm really confused i try'd sloving it but i keep getting it wrong!
• ah i see, you are not focused or it might be like, as easy as water. i can explain:

he wants to find who started higher, nick or alyssa

in this case here they have given the formula: a = 1/3t + 5.

We need to find out alyssa's height using this formula and we know that when t = 0 then that is where alyssa started at.

so lets punch in the value's: a = 1/3(0) + 5
Whereas in the equation above you might be thinking what that 0 is.

the 0 represents t(time)

so whenever a number is multiplied by a 0 your answer is a 0 no matter what.

then when we solve it: a = 1/3*0 which refers to 0
finally the equation for alyssa's height is: a = 0 + 5 = 5

Thats it: alyssa's height when she started off was: 5

now lets solve for nick's height and from where he started off from.

they give a table:
t(time) | Nicks height
6 | 6
8 | 7
10| 8

lets see the change in y(nicks height) and x(time nick took) : when there is a change of 1 in y, there was change of 2 in x. so now we know what happens when there is a change in y.

and thats how we can finally find what nicks height is when he started at 0 on the time.

lets go in reverse until we reach 0:
6-2 = 4

the number 6 in the equation represents time and the number 2 that is in the equation is the change it takes per 1 change in nicks height

so now we have 4 and what is nicks height it is 5 because a decrease of 2 in time is a decrease by 1 in nicks height so lets continue doing the same thing over and over again till we reach 0.

4(time)-2(change in time per 1 change in y(nicks height)) = 2
the height of nick now is: 4

Lets do it again: 2(time)-2(change in time per 1 change in y(nicks height) = 0

the height of nick now is 3.

finally we found nicks height when he started off, it is 3!

just a side note: that the numbers i was using as time were those from the original time - 2 and thats how i found it.

hope i solved your problem and any problems and further questions: ask i will be there

hope this helps
(1 vote)
• Do we know the formula of the slope?
(1 vote)
• Which 6 is he using for n? Is he using the same 6 as time or is he using the 6 for Nick's height? Can someone please break this down for me?
(1 vote)
• I don't get the equation. Why the 1/3 times t?
• 1/3 is the amount of feet Alyssa climbs per second. And t represents the amount of seconds that has passed. So therefore it is
1/3 * t

The 5 is how high far she is when she first started climbing, or when t = 0
(1 vote)
• Were substitute "0" for "t".
a=1/3(0)+5
(1 vote)
• yes! it is definitly 0 because we need to find the y intercept on where alyssa started, and so it is 5 because you have to find from where she started from
(1 vote)
• 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)
• 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)?