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3 years ago

Lisa takes 3 hours to mow the lawn, while her cousin, Barb, takes 2 hours. How long will it take them working together?

Mathematics

2 answers:

Colt1911 [192]3 years ago

5 0

Answer:6 hours

Step-by-step explanation:

3x2=6

RSB [31]3 years ago

4 0

Answer:

t=72 minutes

Step-by-step explanation:

If it takes Lisa 3 hours to mow the lawn, then she mows 13 of the lawn per hour. Barb takes 2 hours to do it alone so she completes 12 of the lawn each hour. Working together, they mow the lawn in some time t. This can be written as

$\frac{1}{3}$ + $\frac{1}{2}$ = $\frac{1}{t}$

Multiply each side by the least common denominator, 6t.

6t( $\frac{1}{3}$ + $\frac{1}{2}$ )=6t( $\frac{1}{t}$ )

Simplify and solve.

2t+3t=6

We can multiply the fraction by 60 to convert the fraction of an hour to minutes.

t= $\frac{6}{5}$ (60 minutes)

To mow the lawn, it takes the two working together

t=72 minutes.

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3 years ago

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y=1.5x+3

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1 year ago

A metal beam was brought from the outside cold into a machine shop where the temperature was held at 65degreesF. After 5 min, t

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Answer:

The beam initial temperature is 5 °F.

Step-by-step explanation:

If T(t) is the temperature of the beam after t minutes, then we know, by Newton’s Law of Cooling, that

$T(t)=T_a+(T_0-T_a)e^{-kt}$

where $T_a$ is the ambient temperature, $T_0$ is the initial temperature, $t$ is the time and $k$ is a constant yet to be determined.

The goal is to determine the initial temperature of the beam, which is to say $T_0$

We know that the ambient temperature is $T_a=65$ , so

$T(t)=65+(T_0-65)e^{-kt}$

We also know that when $t=5 \:min$ the temperature is $T(5)=35$ and when $t=10 \:min$ the temperature is $T(10)=50$ which gives:

$T(5)=65+(T_0-65)e^{k5}\\35=65+(T_0-65)e^{-k5}$

$T(10)=65+(T_0-65)e^{k10}\\50=65+(T_0-65)e^{-k10}$

Rearranging,

$35=65+(T_0-65)e^{-k5}\\35-65=(T_0-65)e^{-k5}\\-30=(T_0-65)e^{-k5}$

$50=65+(T_0-65)e^{-k10}\\50-65=(T_0-65)e^{-k10}\\-15=(T_0-65)e^{-k10}$

If we divide these two equations we get

$\frac{-30}{-15}=\frac{(T_0-65)e^{-k5}}{(T_0-65)e^{-k10}}$

$\frac{-30}{-15}=\frac{e^{-k5}}{e^{-k10}}\\2=e^{5k}\\\ln \left(2\right)=\ln \left(e^{5k}\right)\\\ln \left(2\right)=5k\ln \left(e\right)\\\ln \left(2\right)=5k\\k=\frac{\ln \left(2\right)}{5}$

Now, that we know the value of $k$ we can use it to find the initial temperature of the beam,

$35=65+(T_0-65)e^{-(\frac{\ln \left(2\right)}{5})5}\\\\65+\left(T_0-65\right)e^{-\left(\frac{\ln \left(2\right)}{5}\right)\cdot \:5}=35\\\\65+\frac{T_0-65}{e^{\ln \left(2\right)}}=35\\\\\frac{T_0-65}{e^{\ln \left(2\right)}}=-30\\\\\frac{\left(T_0-65\right)e^{\ln \left(2\right)}}{e^{\ln \left(2\right)}}=\left(-30\right)e^{\ln \left(2\right)}\\\\T_0=5$

so the beam started out at 5 °F.

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