Mr. Robinson traveled to a city 210 miles from his home to attend a meeting. Due to car trouble, his average speed returning was 9 mph less than his speed going. If the total time for the round trip was 6 hours, at what rate of speed did he travel to the city

the average speed at which he traveled to the city is 74.8 mph

Step-by-step explanation:

Let x represent the rate or speed at which he traveled to the city. Due to car trouble, his average speed returning was 9 mph less than his speed going. It means that the speed at which he returned is (x - 9) mph.

Time = distance/speed

Assuming the distance travelled to and from the city is the same ie 210 miles, then

Time spent in travelling to the city is

210/x

Time spent in travelling back from the city is

210/(x - 9)

If the total time for the round trip was 6 hours, it means that

210/x + 210/(x - 9) = 6

Multiplying both sides of the equation by x(x - 9), it becomes

210(x - 9) + 210x = 6x(x - 9)

210x - 1890 + 210x = 6x² - 54x

6x² - 54x - 210x - 210x + 1890 = 0

6x² - 474x + 1890 = 0

We would apply the general formula for solving quadratic equations which is expressed as

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 6

b = - 474

c = 1890

Therefore,

x = [- - 474 ± √(- 474² - 4 × 6 × 1890)]/2 × 6

x = [474 ± √(224676 - 45360)]/12

x = [474 ± √179316]/12

x = (474 + 423.5)/14 or x = (474 - 423.5)/12

x = 74.8 or x = 4.2

Checking,

For x = 74.8

210/74.8 + 210/(74.8 - 9) = 6

= 2.8 + 3.2 = 6

Therefore, x = 74.8 mph

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !