Emily drove to town with an average speed of 32 miles per hour, and then back home with an average speed of 38 miles per hour. If her total traveling time was 42 minutes, how far is it from home to town?

Step-by-step explanation:

Speed - s,   Distance - d,  Time - t

Equation of time is:

Given,

Total time is the sum of time values to and from the town:

It is given that,

→ s1= 32 miles/h

→ s2 = 38 miles/h

Now t1 + t2 is,

→ 42 min

→ 42/60 hours

→ 7/10 hours

The formula we use,

→ Time = Distance/Speed

→ t = d/s

Then the total time is the,

Sum of time values to and from the town.

→ d/32 + d/38 = 7/10

→ d/16 + d/19 = 7/5

→ d{(1/16) + (1/19)} = 7/5

→ d(16 + 19) = (7/5) × (16 × 19)

→ 35d = 425.6

→ d = 425.6/35

→ d = 12.16

Hence, the distance is 12.16 miles.

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.