Question

Select the correct answer from each drop-down menu.
Ted writes an equation to represent the number of stairs he climbs, s, in terms of the time in seconds, t, it takes him to climb those stairs.
s = 5/6 t
Michael, on the other hand, creates a table to record the time in seconds it took him to walk up a different numbers of stairs.
Assume that Ted and Michael both climb the same set of stairs and that they climb at a constant rate. Ted’s approximate climbing rate is (???) stairs per second, and Michael’s rate is (???) stairs per second.
On a graph of these relationships, the line relating the number of stairs that Michael climbed with respect to time would be (???) Ted’s line. So, Ted’s climbing speed is (???) Michael’s.
Answer Choices:
Blank 1: 0.75, 0.83, 0.9, or 0.94
Blank 2: 0.75, 0.83, 0.9, or 0.94
Blank 3: steeper than, less steep than, or as steep as
Blank 4: slower than, faster than, or equal to
(See image attachment.)

Answer 1

Answer:

1. 0.83
2. 0.9
3. steeper than
4. slower than

Step-by-step explanation:

Letting t=1 in Ted's equation, we find that he climbs 5/6 stairs in 1 second. As a decimal, 5/6 ≈ 0.83.

Michael climbs 9 stairs in 10 seconds so his rate is ...

... (9 stairs)/(10 seconds) = (9/10) stairs/second = 0.9 stairs/second

Michael's graph will be a line with a slope of 0.9; Ted's graph will be a line with a slope of about 0.83, so the line on Michael's graph is steeper.

Ted climbs fewer stairs per second, so his rate is slower than Michael's.

_____

Comment on the problem

You're being asked to compare two different rates that are associated with two different people. First the comparison is one way, then it is the other way. This can be confusing. It might be helpful to draw and label a simple chart to help you keep it straight. (The attachment is such a chart scribbled on a bit of scratch paper. It is sufficient for the purpose.)

Answer 2

0.83

0.9

steeper than

slower than

Step-by-step explanation:

Letting t=1 in Ted's equation, we find that he climbs 5/6 stairs in 1 second. As a decimal, 5/6 ≈ 0.83.

Michael climbs 9 stairs in 10 seconds so his rate is ...

... (9 stairs)/(10 seconds) = (9/10) stairs/second = 0.9 stairs/second

Michael's graph will be a line with a slope of 0.9; Ted's graph will be a line with a slope of about 0.83, so the line on Michael's graph is steeper.

Ted climbs fewer stairs per second, so his rate is slower than Michael's.

_____

Comment on the problem

You're being asked to compare two different rates that are associated with two different people. First the comparison is one way, then it is the other way. This can be confusing. It might be helpful to draw and label a simple chart to help you keep it straight. (The attachment is such a chart scribbled on a bit of scratch paper. It is sufficient for the purpose.)