Question

Lucia is using energy at a rate of 420 kilocalories (kcal) per hour (h) ice skating. At what rate is lucla using energy in calories per minute (cals/mins)?

Answer 1

1 / 3

We will convert 420\,\dfrac{\text{kcal}}{\text{h}}420

h

kcal

​ 420, space, start fraction, k, c, a, l, divided by, h, end fraction to a rate in \dfrac{\text{cal}}{\text{min}}

min

cal

​ start fraction, c, a, l, divided by, m, i, n, end fraction using the following conversion rates:

There are 60\text{ min}60 min60, space, m, i, n per 1\text{ h}1 h1, space, h.

There are 1000\text{ cal}1000 cal1000, space, c, a, l per 1\text{ kcal}1 kcal1, space, k, c, a, l.

Hint #22 / 3

\begin{aligned} &\phantom{=} \dfrac{420 \text{ kcal}}{1\text{ h}} \cdot\dfrac{1\text{ h}}{60\text{ min}}\cdot\dfrac{1000\text{ cal}}{1\text{ kcal}} \\\\ &=\dfrac{420\cdot 1 \cdot 1000 \cdot \cancel{\text{kcal}}\cdot\cancel{\text{h}} \cdot \text{cal}}{1\cdot 60 \cdot 1\cdot\cancel{\text{h}}\cdot \text{min} \cdot \cancel{\text{kcal}} } \\\\ &=\dfrac{420{,}000}{60}\,\dfrac{\text{cal}}{\text{min}} \\\\ &=7000\,\dfrac{\text{cal}}{\text{min}} \end{aligned}

​

=

1 h

420 kcal

​ ⋅

60 min

1 h

​ ⋅

1 kcal

1000 cal

​

=

1⋅60⋅1⋅

h

⋅min⋅

kcal

420⋅1⋅1000⋅

kcal

⋅

h

⋅cal

​

=

60

420,000

​

min

cal

​

=7000

min

cal

​

​

Hint #33 / 3

In conclusion, Lúcia is using energy in \dfrac{\text{cal}}{\text{min}}

min

cal

​ start fraction, c, a, l, divided by, m, i, n, end fraction at a rate of:

7000\,\dfrac{\text{cal}}{\text{min}}7000

min

cal

​

Answer 2

we know that

`1\ kilocalories=1,000\ calories\\ 1\ hour=60\ minutes`

1) Convert
`(kcal)/(h)` to
`(cal)/(h)`

`420(kcal)/(h)=420*1,000=420,000(cal)/(h)`

2) Convert
`(cal)/(h)` to
`(cal)/(min)`

`420,000(cal)/(h)=420,000/60=7,000(cal)/(min)`

therefore

the answer is

`7,000(cal)/(min)`