Answer: 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
