Answer: The speed at which he traveled to the city is 69.8 mph
Step-by-step explanation:
Let x represent the speed at which he traveled to the city.
Mr. Smith traveled to a city 300 miles from his home to attend a meeting.
Time = distance/speed
Time taken to travel to the city is
300/x
Due to car trouble, his average speed on returning was 6 mph less than his speed going. This means that the speed at which he returned is (x - 6) mph. Time taken to return from the city is
300/(x - 6)
If the total time for the round trip was 9 hours, it means that
300/x + 300/(x - 6) = 9
Cross multiplying by x(x - 6), it becomes
300(x - 6) + 300x = 9x(x - 6)
300x - 1800 + 300x = 9x² - 54x
9x² - 54x - 300x - 300x - 1800 = 0
9x² - 654x -1800 = 0
Applying the general quadratic equation,
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 9
b = - 654
c = 1800
Therefore,
x = [- - 654 ± √(- 654² - 4 × 9 × 1800)]/2 × 9
x = [654 ± √(427716 - 64800)]/18
x = [654 ± √362916.4]/18
x = (654 + 602.4)/2 or x = (654 - 602.4)/18
x = 1256.4/18 or x = 51.6/18
x = 69.8mph or x = 2.9 mph
The speed at which he traveled to the city is 69.8 mph
By checking,
Time spent travelling to the city = 300/69.8 = 4.3 hours
Time spent returning =
300/(69.8 - 6) = 4.7 hours
4.3 + 4.7 = 9 hours
