Final answer:
The statement is False. Increasing the speed of a car by 10 km/h does not reduce the time of a journey for a distance of 72 km by 3 minutes.
Step-by-step explanation:
The statement is False.
To determine whether the time of a journey is reduced by increasing the speed of a car, we need to analyze the relationship between speed, distance, and time. According to the question, increasing the speed of the car by 10 km/h reduces the journey time by 3 minutes for a distance of 72 km. Let's calculate the original and new time taken to complete the journey:
- Original Time: t1 = Distance/Speed = 72 km / (Speed)
- New Time: t2 = Distance/(Speed + 10 km/h) = 72 km / (Speed + 10 km/h)
Since t2 is reduced by 3 minutes, we can write the equation:
t1 - t2 = 3 minutes
Plugging in the equations from steps 1 and 2:
72 km / (Speed) - 72 km / (Speed + 10 km/h) = 3 minutes
To solve this equation, we need to convert the time units to the same format. Let's convert the minutes to hours:
3 minutes = 3 minutes / 60 minutes/hour = 0.05 hours
Now, we can solve the equation:
72 km / Speed - 72 km / (Speed + 10 km/h) = 0.05 hours
To simplify the equation, we can multiply through by Speed * (Speed + 10 km/h) to eliminate the denominators:
(72 km / Speed) * (Speed * (Speed + 10 km/h)) - (72 km / (Speed + 10 km/h)) * (Speed * (Speed + 10 km/h)) = 0.05 hours * (Speed * (Speed + 10 km/h))
Cancelling out the common terms:
72 km * (Speed + 10 km/h) - 72 km * Speed = 0.05 hours * (Speed * (Speed + 10 km/h))
Simplifying further:
72 km * 10 km/h = 0.05 hours * (Speed * (Speed + 10 km/h))
720 km/h = 0.05 hours * (Speed * (Speed + 10 km/h))
Now, we can solve for Speed:
0.05 hours * (Speed * (Speed + 10 km/h)) = 720 km/h
0.05 (Speed * (Speed + 10 km/h)) = 720
(Speed * (Speed + 10 km/h)) = 720 / 0.05
(Speed * (Speed + 10 km/h)) = 14400
Simplifying further:
Speed * (Speed + 10 km/h) = 14400
Speed^2 + 10 Speed - 14400 = 0
Using the quadratic formula:
Speed = (-10 + sqrt(100 + 4 * 14400)) / 2
Speed = (-10 + sqrt(100 + 57600)) / 2
Speed = (-10 + sqrt(57700)) / 2
Calculating the Speed:
Speed = (-10 + 240) / 2 = 230 / 2 = 115 km/h
The original speed of the car is 115 km/h. Therefore, increasing the speed by 10 km/h results in a speed of 125 km/h. However, the time is not reduced by 3 minutes as stated in the question. Therefore, the statement is False.