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)?

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

3+x

step-by-step explanation:

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of