Answer: the average speed at which he traveled to the city is 52.9 mph
Step-by-step explanation:
Let x represent the average speed at which he traveled to the city. Due to car trouble, his average speed returning was 8mph less than his speed going. It means that the speed at which he returned is (x - 8) mph.
Time = distance/speed
Assuming the distance travelled to and from the city is the same(170 miles), then
Time spent in travelling to the city is
170/x
Time spent in travelling back from the city is
170/(x - 8)
If the total time for the round trip was 7 hours, it means that
170/x + 170/(x - 8) = 7
Multiplying both sides of the equation by x(x - 8), it becomes
170(x - 8) + 170x = 7x(x - 8)
170x - 1360 + 170x = 7x² - 56x
7x² - 56x - 170x - 170x + 1360 = 0
7x² - 396x + 1360 = 0
Applying the general formula for solving quadratic equations which is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 7
b = - 396
c = 1360
Therefore,
x = [- - 396 ± √(- 396² - 4 × 7 × 1360)]/2 × 7
x = [396 ± √(156816 - 38080)]/14
x = [396 ± √118736]/14
x = (396 + 344.58)/14 or x = (396 - 344.58)/14
x = 52.9 or 3.7
Checking both values of x,
For x = 52.9
170/52.9 + 170/(52.9 - 8) = 7
= 3.2 + 3.8 = 7
Therefore, x = 52.9 mph
