Question

On Monday Carla runs 2 5/8 in 15 minutes

Answer 1

Answer:

(a) 10.5 miles/hour

(b) 6.5 miles

Step-by-step explanation:

(a)

Carla runs $2\frac{5}{8}=\dfrac{21}{8}$

time taken by Carla=15 minutes=15/60 hours.

Hence Average rate of speed = total distance/total time

                                        =$\dfrac{21}{8}\times\dfrac{60}{15}\\\\=10.5$

Hence, the average rate of speed in miles per hour is 10.5 miles/hour.

(b)

on Tuesday Carla decides to jog instead of walk and decreases her speed by 20%(20/100=0.2).

so her speed=10.5-0.2×10.5

                     =8.4 miles/hour.

Now distance travelled by her in 50 minutes(50/60 hours)=8.4×(50/60) miles

                  =6.5 miles.

Answer 2

Answer:

(A)

$v=\frac{7}{42240}mph$

(B)

$d=\frac{7}{63360}miles$

Step-by-step explanation:

(A)

We are given

distance traveled is

$=2\frac{5}{8}= \frac{8\times 2+5}{8}=\frac{21}{8}in$

we know that

1 inch = $\frac{1}{12}feet$

We can multiply both sides by 21/8

$\frac{21}{8}in=\frac{1}{12}\times \frac{21}{8} feet$

$\frac{21}{8}in=\frac{7}{32}feet$

so,

$d=\frac{7}{32}feet$

we know that

1 mile =5280 feet

$d=\frac{7}{32}\times\frac{1}{5280} miles$

$d=\frac{7}{168960}mile$

time is 15 minutes

we know that

160 min =1 hour

so,

$15min=\frac{15}{60}hour$

$15min=\frac{1}{4}hour$

$t=\frac{1}{4}hour$

now, we can find speed

$v=\frac{d}{t}$

now, we can plug values

$v=\frac{\frac{7}{168960}}{\frac{1}{4}}$

now, we can simplify it

$v=\frac{7}{42240}mph$

(B)

On Tuesday Carla decides to jog instead of run and so decreases her average rate of speed by 20 percent

so, average speed becomes

$v=\frac{7}{42240}\times\frac{80}{100} mph$

$v=\frac{7}{52800}mph$

We are given

time =50 min

now, we can find time in hour

$t=\frac{50}{60}hr= \frac{5}{6}hr$

we know that

distance = (velocity)*(time)

we get

$d=\frac{7}{52800}\times \frac{5}{6}miles$

$d=\frac{7}{63360}miles$