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damaskus [11]
2 years ago
12

A relay race is 1/10 kilometer long. Four athletes will run an equal distance to complete the relay. How far does each athlete r

un ?

Mathematics
2 answers:
Over [174]2 years ago
8 0
25 metres. Because 1/10th of a kilometre is a 100 metres. And four athletes divided by 100 metres is 25 metres.
lutik1710 [3]2 years ago
8 0

Answer:

25 meters.

Step-by-step explanation:

Let us suppose each athlete run x km.

Hence, four athlete will run 4x km.

Now, the distance of the relay race is 1/10 km

Thus, we have

4x=\frac{1}{10}

Divide both sides by 4

x=\frac{1}{40}km

Now, 1 km = 1000 meters. Thus, we have

x=\frac{1}{40}\times1000\\\\x=25

Thus, each athlete run 25 meters.

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(y - 2)(y + 2)

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2 years ago
a mechanic worked 20 hours. another mechanic worked 15 hours. together they charged a total of $1950. what was the rate charged
Natasha_Volkova [10]

Answer: The mechanics both charged $70 and $45 per hour respectively

Step-by-step explanation: We shall start by calling the mechanics hourly rates x and y respectively. So if one worked for 20 hours and charged 20 times x dollars, and the other one worked for 15 hours and charged 15 times y dollars, totalling 1950 dollars, we can write the following expression,

20x + 15y = 1950

Also, if the sum of the two rates was 115 dollars, that means for working for an hour only, they both would earn

x + y = 115

We now have a pair of simultaneous equations

20x + 15y = 1950 --------(1)

x + y = 115 ------------------(2)

We shall use the substitution method for this problem.

From equation (2), make x the subject of the equation

x = 115 - y

Substitute for the value of x into equation (1)

20(115 - y) + 15y = 1950

2300 - 20y + 15y = 1950

By collecting like terms we now have

2300 - 1950 = 20y - 15y

(Note that when a negative value crosses to the other side of the equation, it becomes a positive value and vice versa)

350 = 5y

Divide both sides of the equation by 5

70 = y

We now substitute for the value of y into equation (2)

x + y = 115

x + 70 = 115

Subtract 70 from both sides of the equation

x = 45.

Therefore, the rate they charged per hour were $45 and $70 respectively.

7 0
3 years ago
A machine at a bottling company fills water bottles. the number of bottles filled is proportional to the amount of time the mach
Whitepunk [10]

In the table shown below:

Let N be the number of bottles filled,

Let T be the time in hours.

Given that the number of bottles filled is proportional to the amount of time the machine runs, we have

\begin{gathered} N\propto T \\ \text{Introducing a proportionality constant, we have } \\ N\text{ = kT} \\ \Rightarrow k\text{ = }\frac{N}{T} \\  \end{gathered}

Let's evaluate the value of k for each day.

Thus, on monday,

\begin{gathered} N\text{ = 9900} \\ T\text{ = 5.5} \\ \text{thus,} \\ k\text{ = }\frac{9900}{5.5} \\ \Rightarrow k\text{ = 1800} \end{gathered}

Tuesday:

\begin{gathered} N\text{ = }11160 \\ T\text{ = }6.2 \\ \text{thus,} \\ k\text{ = }\frac{11160}{6.2} \\ \Rightarrow k\text{ = 1800} \end{gathered}

Wednesday:

\begin{gathered} N\text{ = }12330 \\ T\text{ = }6.25 \\ \text{thus,} \\ k\text{ = }\frac{12330}{6.25} \\ \Rightarrow k\text{ = 1972.8} \end{gathered}

Thursday:

\begin{gathered} N\text{ = }10440 \\ T\text{ = }5.80 \\ \text{thus,} \\ k\text{ = }\frac{10440}{5.8} \\ \Rightarrow k=1800 \end{gathered}

It is observed that all exept wednesday have the same value of k.

Thus, the amount of time required for the number of bottles filled on wednesday is evaluated as

\begin{gathered} N\text{ = }12330 \\ k\text{ = 1800} \\ T\text{ = ?} \\ \text{but} \\ k\text{ = }\frac{N}{T} \\ 1800\text{ = }\frac{12330}{T} \\ \Rightarrow T\text{ = }\frac{\text{12330}}{1800} \\ T\text{ = 6.85} \end{gathered}

Hence, the incorrect day is Wednesday. The amount of time for that many bottles should be 6.85 hours.

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Arturiano [62]

Answer:

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<u>The graph is shown in attached image.</u>

<u />

The black line is Juan's graph.

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The end of the curve(s) means the end of the race. Both curve's ending point in y-axis is 4 miles so the end of the race is 4 miles.

But in x-axis, we see the time:

Juan finishes at 13 minutes

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<u>Definitely Juan wins the race</u>

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