A man travels from home to town and back in a motor cycle. He travels to home from town at a speed which is 20 kilometer/hour more than his journey to the town from home. The average speed of his total journey was 48 kilometre/hour. [3] (a) if the distance from home to town is 5 kilometre, find his total journey time. (b) by taking the speed of his journey from home to town as x , form a second degree equations.
Answers
12.5 minutes is total journey time , x² - 28x - 480 = 0
Step-by-step explanation:
speed of his journey from home to town = x km/hr
He travels to home from town at a speed which is 20 kilometer/hour more than his journey to the town from home.
=> Speed of his journey from town to home = x + 20 km/hr
Let say Distance = D km
Time = D/x + D/(x + 20)
Average Speed = 48 km /hr
Time = (D + D)/48 = D/24 hr
D/24 = D/x + D/(x + 20)
=> 1/24 = 1/x + 1/(x + 20)
=> x(x + 20) = 24(x + 20) + 24x
=> x² + 20x =24x + 480 + 24x
=> x² - 28x - 480 = 0
=> x² + 12x - 40x - 480 = 0
=> x(x + 12) - 40(x + 12) =0
=> (x - 40(x + 12) =0
=> x = 40
speed of his journey from home to town = 40 km/hr
Speed of his journey from town to home = 60 km/hr
if the distance from home to town is 5 kilometre, find his total journey time.
= 10/48 hr or (5/40 + 5/60) hr
= 12.5 minutes or (7.5 + 5 = 12.5 minutes)
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