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