Question

Harvey the wonder hamster can run 3\dfrac16 \text{ km}3 6 1 ​ km3, start fraction, 1, divided by, 6, end fraction, space, k, m in \dfrac14 4 1 ​ start fraction, 1, divided by, 4, end fraction hour. Harvey runs at a constant rate. Find his average speed in kilometers per hour.

Answer 1

Given the distance the wonder hamster run = 3 1/6 km.

Time in hours = 1 1/4 hours.

We need to find the average speed of Harvey in kilometers per hour.

We know speed formula

Speed = distance/time.

Plugging value of distance and time in above formula, we get

Average speed = 3 1/6 ÷ 1 1/4

$=3\frac{1}{6}\div \:1\frac{1}{4}$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 3\frac{1}{6}=\frac{19}{6}$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 1\frac{1}{4}=\frac{5}{4}$

$=\frac{19}{6}\div \frac{5}{4}$

$=\frac{19}{6}\times \frac{4}{5}$

$\mathrm{Cross-cancel\:common\:factor:}\:2$

$=\frac{19}{3}\times \frac{2}{5}$

$=\frac{38}{15}$

$=2\frac{8}{15}$

Therefore, average speed of Harvey is $2\frac{8}{15}$ kilometers per hour.

Answer 2

Answer:To find kilometers per hour, we divide kilometers by hours.

Hint #22 / 8

\phantom{=}\dfrac{~~~3 \dfrac16 \text{ km}~~~}{\dfrac14 \text{ hour}}=  

4

1

​  

 hour

  3  

6

1

​  

 km    

​  

empty space, start fraction, space, space, space, 3, start fraction, 1, divided by, 6, end fraction, start text, space, k, m, end text, space, space, space, divided by, start fraction, 1, divided by, 4, end fraction, start text, space, h, o, u, r, end text, end fraction

Hint #33 / 8

= 3 \dfrac{1}6 \div \dfrac14\qquad=3  

6

1

​  

÷  

4

1

​  

equals, 3, start fraction, 1, divided by, 6, end fraction, divided by, start fraction, 1, divided by, 4, end fraction [Explain]

Hint #44 / 8

= \dfrac{19}6 \div \dfrac14\qquad=  

6

19

​  

÷  

4

1

​  

equals, start fraction, 19, divided by, 6, end fraction, divided by, start fraction, 1, divided by, 4, end fraction [Explain]

\phantom{=}3 \dfrac{1}6  

empty space, 3, start fraction, 1, divided by, 6, end fraction

= \dfrac{6}{6} + \dfrac{6}{6} +\dfrac{6}{6} +\dfrac{1}{6}  

 

 

 

equals, start fraction, 6, divided by, 6, end fraction, plus, start fraction, 6, divided by, 6, end fraction, plus, start fraction, 6, divided by, 6, end fraction, plus, start fraction, 1, divided by, 6, end fraction

= \dfrac{19}{6}  

equals, start fraction, 19, divided by, 6, end fraction

Hint #55 / 8

= \dfrac{19}{6} \cdot \dfrac41\qquad=  

6

19

​  

⋅  

1

4

​  

equals, start fraction, 19, divided by, 6, end fraction, dot, start fraction, 4, divided by, 1, end fraction [Explain]

\dfrac14  

start fraction, 1, divided by, 4, end fraction\dfrac41  

start fraction, 4, divided by, 1, end fraction

Hint #66 / 8

=\dfrac{76}{6}\qquad=  

6

76

​  

equals, start fraction, 76, divided by, 6, end fraction [Explain]

\phantom{=}\dfrac{19}{6} \cdot \dfrac41  

 

empty space, start fraction, 19, divided by, 6, end fraction, dot, start fraction, 4, divided by, 1, end fraction

=\dfrac{19 \cdot 4}{6 \cdot 1}  

equals, start fraction, 19, dot, 4, divided by, 6, dot, 1, end fraction

=\dfrac{76}{6}  

equals, start fraction, 76, divided by, 6, end fraction

Hint #77 / 8

=\dfrac{38}{3}=  

3

38

​  

equals, start fraction, 38, divided by, 3, end fraction kilometers per hour \qquad [Explain]

\phantom{=}\dfrac{76}{6}  

empty space, start fraction, 76, divided by, 6, end fraction

= \dfrac{38 \cdot \cancel{2}}{3 \cdot \cancel{2}}  

 

 

equals, start fraction, 38, dot, start cancel, 2, end cancel, divided by, 3, dot, start cancel, 2, end cancel, end fraction

= \dfrac{38}{3}  

equals, start fraction, 38, divided by, 3, end fraction

Hint #88 / 8

Harvey averages \dfrac{38}{3}  

3

38

​  

start fraction, 38, divided by, 3, end fraction kilometers per hour.

Step-by-step explanation: