A bus takes 195 minutes to travel a distance of (2x + 30) km at an average speed of (x – 20) km/h. Calculate the actual distance traveled.
distance =time×speed
(X-20)(3.25)=2x+30
3.25x-2x=30+65
1.25=95
95÷1.25=76
as always, distance = speed * time.
(x-20)(3.25) = 2x+30
x = 76
So, 56 km/hr * 3.25 hr = 182 km
It good
To calculate the actual distance traveled, we need to use the formula:
Distance = Speed × Time
Given:
Time = 195 minutes
Speed = (x - 20) km/h
To calculate the distance, we first need to convert the time from minutes to hours. Since there are 60 minutes in an hour, we divide the given time by 60:
Time = 195 minutes ÷ 60 = 3.25 hours
Now, we can substitute the values of time and speed into the formula:
Distance = (x - 20) km/h × 3.25 hours
Next, we need to express the distance in terms of x. We are given the expression (2x + 30) km for the distance traveled. So we set this expression equal to the calculated distance:
2x + 30 = (x - 20) × 3.25
To solve this equation, we distribute 3.25 to each term in the parentheses:
2x + 30 = 3.25x - 65
Next, we bring like terms together by subtracting 2x from both sides of the equation:
30 = 3.25x - 2x - 65
Combine the x terms:
30 = 1.25x - 65
Add 65 to both sides:
95 = 1.25x
Finally, divide both sides by 1.25 to solve for x:
x = 95 / 1.25
Simplifying:
x = 76
Now that we have found the value of x, we can substitute it back into the expression for distance to calculate the actual distance traveled:
Distance = 2x + 30
Distance = 2(76) + 30
Distance = 152 + 30
Distance = 182 kilometers
Therefore, the actual distance traveled by the bus is 182 kilometers.