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Sagot :
Answer:
Jacob finished the race faster than Daniel.
Step-by-step explanation:
We have that,
Daniel completed the hurdle in [tex]\frac{3}{4}[/tex] of a minute i.e. 75% of a minute.
Jacob completed the hurdle with [tex]\frac{5}{12}[/tex] 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 [tex]\frac{5}{12}[/tex] 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
Further explanation
Given:
At a track meet, Jacob and Daniel compete in 220 m hurdles.
Daniels finishes in [tex]\frac{3}{4}[/tex] of the a min.
Jacob finishes with [tex]\frac{5}{12}[/tex] 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.
[tex]\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}[/tex] 12 units represent in one minute.
Daniels finishes in [tex]\frac{3}{4}[/tex] of the a min.
[tex]\frac{3}{4} = \frac{9}{12}} \rightarrow \boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}[/tex] or 9 of 12 units.
Jacob finishes with [tex]\frac{5}{12}[/tex] of a min remaining, or 5 of 12 units. This means Jacob finishes in [tex]\frac{7}{12}[/tex] or 7 of 12 units, that is [tex]\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}[/tex]
And now we conclude who ran the race in a faster time.
Daniels: [tex]\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}[/tex]
Jacobs: [tex]\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}[/tex]
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 [tex]\boxed{ \ \frac{3}{4} = \frac{9}{12} \ }[/tex] of the a min.
[tex]\boxed{\frac{9}{12} \times 60 \ minutes = 45 \ seconds}[/tex]
Jacob: in [tex]\boxed{ \ 1 - \frac{5}{12} = \frac{7}{12} \ }[/tex] of the a min.
[tex]\boxed{\frac{7}{12} \times 60 \ minutes = 35 \ seconds}[/tex]
Jacob's time is shorter, so he's the fastest.
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Calculate the speed
Recall [tex]\boxed{speed = distance \div time}[/tex]
Daniels: [tex]\boxed{speed = 220 \ m \div 45 \ seconds = 4\frac{8}{9} \ m/s \ }[/tex]
Jacob: [tex]\boxed{speed = 220 \ m \div 35 \ seconds = 6\frac{2}{7} \ m/s \ }[/tex]
Thus, Jacob's speed proved greater than Daniels's speed.
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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
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