Answered

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?

Verified Answer :

Answer:

Jacob finished the race faster than Daniel.

Step-by-step explanation:

We have that,

Daniel completed the hurdle in \(\frac{3}{4}\) of a minute i.e. 75% of a minute.

Jacob completed the hurdle with \(\frac{5}{12}\) 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 \(\frac{5}{12}\) 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.

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Jacob

Further explanation

Given:

At a track meet, Jacob and Daniel compete in 220 m hurdles.

Daniels finishes in \(\frac{3}{4}\) of the a min.

Jacob finishes with \(\frac{5}{12}\) 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.

\(\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\) 12 units represent in one minute.

Daniels finishes in \(\frac{3}{4}\) of the a min.

\(\frac{3}{4} = \frac{9}{12}} \rightarrow \boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\) or 9 of 12 units.

Jacob finishes with \(\frac{5}{12}\) of a min remaining, or 5 of 12 units. This means Jacob finishes in \(\frac{7}{12}\) or 7 of 12 units, that is \(\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\)

And now we conclude who ran the race in a faster time.

Daniels: \(\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\)  

Jacobs: \(\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\boxed{\circ}\)

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 \(\boxed{ \ \frac{3}{4} = \frac{9}{12} \ }\) of the a min.

\(\boxed{\frac{9}{12} \times 60 \ minutes = 45 \ seconds}\)

Jacob: in \(\boxed{ \ 1 - \frac{5}{12} = \frac{7}{12} \ }\) of the a min.

\(\boxed{\frac{7}{12} \times 60 \ minutes = 35 \ seconds}\)

Jacob's time is shorter, so he's the fastest.

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Calculate the speed

Recall \(\boxed{speed = distance \div time}\)

Daniels: \(\boxed{speed = 220 \ m \div 45 \ seconds = 4\frac{8}{9} \ m/s \ }\)

Jacob: \(\boxed{speed = 220 \ m \div 35 \ seconds = 6\frac{2}{7} \ m/s \ }\)

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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