Answer:
Jacob finished the race faster than Daniel.
Step-by-step explanation:
We have that,
Daniel completed the hurdle in of a minute i.e. 75% of a minute.
Jacob completed the hurdle with remaining of a minute i.e. 41.7% remaining of a minute.
Now, as we have that,
75% of a minute = 45 seconds
41.7% of a minute = 25 seconds
Since, Jacob had time remaining.
Thus, Jacob had = 60 - 25 = 35 seconds remaining.
So, Daniel ran in 45 seconds and Jacob ran in 35 seconds.
Hence, we get that, Jacob finished the race faster than Daniel.
Jacob
Given:
At a track meet, Jacob and Daniel compete in 220 m hurdles.
Daniels finishes in of the a min.
Jacob finishes with of a min remaining.
Question:
Who ran the race in faster time?
The Process:
Let us see the denominators. The least common multiple (LCM) of 4 and 12 is 12.
Let us draw the diagram that represents a minute.
12 units represent in one minute.
Daniels finishes in of the a min.
or 9 of 12 units.
Jacob finishes with of a min remaining, or 5 of 12 units. This means Jacob finishes in or 7 of 12 units, that is
And now we conclude who ran the race in a faster time.
Daniels:
Jacobs:
Because Jacob took the race in a shorter time, he was who ran the race in a faster time.
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Quick Steps
Daniels: in of the a min.
Jacob: in of the a min.
Jacob's time is shorter, so he's the fastest.
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Calculate the speed
Recall
Daniels:
Jacob:
Thus, Jacob's speed proved greater than Daniels's speed.
Keywords: at a track meet, Jacob and Daniel, compete in 220 m hurdles, Daniels, finishes, in 3/4 of the a min, Jacob, finishes, with 5/12 of a min, remaining, who, ran, the race, in faster time, diagram
Answer:
Part 1) The equation of the line is
Part 2) The graph in the attached figure
Step-by-step explanation:
Part 1)
Find the equation of the line
we know that
The equation of a line in slope intercept form is equal to
where
m is the slope
b is the y-intercept
In this problem we have
substitute
Part 2)
Graph the line
Find the intercepts
The y-intercept is the point -----> given value
The x-intercept is the value of x when the value of y is equal to zero
For y=0
The x-intercept is the point
To graph the line plot the intercepts
see the attached figure
The equation for the first club is:
y = 5x + 20 (where x is the number of hikes you go on)
The equation for the second club is:
y = 7x
By "economical", it means which club gives the best deal (meaning you not having to spend too much money). If we want to make the first club economical, we want to find how many hikes it takes to make the second club more expensive.
Let's make the two equations equal each other:
5x + 20 = 7x
Subtract 5x from both sides:
20 = 2x
Divide by 2:
x = 10
10 hikes is when the cost for each club is the same. Anything over that, then, makes the first club economical.
So, the answer would be:
x > 10