How long does it take an automobile traveling in the left lane at 60.0 km/h to overtake (become even with) another car that is traveling in the right lane at 40.0 km/h when the cars’ front bumpers are initially 100 m apart?
I don't think either of your responses is correct. I don't think my hint is correct, either.
distance = rate x time
distance traveled by 40 km/hr car is
d = 40t. solve for t = d/40
distance traveled by 60 km/hr car is
d + 100 = 60t. solve for t = (d+100)/60
The times are equal. Set them equal to each other and solve for distance, then solve for time it takes for the car traveling at 60 km/h to travel d + 100.
Simplify the question. How long does it take a car traveling at 60 km/h to travel 100 m?
9s
3.6s!
nevermind, the previous one is correct. how would I go on about that?
Aren't you suppose to convert km to m (since the distance is in m)?
Yes, you may convert 100 m to 0.1 km in which case d will be in km or you may convert 40 km/h and 60 km/h to m/h and d is then in meters. However, since both 40 km/h and 60 km/h are on opposite sides of the equation, the conversion factor cancels and what I set up above gives the same answer with or without the conversion. Probably the math people won't like that because it isn't good math and I recommend the conversions.
Subtract the velocity of the slower car from the first; this is the relative velocity. Time is distance over velocity, so calculate how long it takes a car to travel 100 meters going 20.0 m/s. The answer is 18s.
To determine the time it takes for the automobile traveling in the left lane to overtake the car in the right lane, we can use the relative velocity of the two cars. The relative velocity is the difference in their speeds.
First, let's convert the speeds of the cars from km/h to m/s.
Speed of the car in the left lane = 60.0 km/h = 60.0 * (1000/3600) m/s = 16.67 m/s
Speed of the car in the right lane = 40.0 km/h = 40.0 * (1000/3600) m/s = 11.11 m/s
The relative velocity is given by the difference in the speeds:
Relative velocity = 16.67 m/s - 11.11 m/s = 5.56 m/s
Now, we need to determine how long it takes for the two cars' front bumpers to be even. We can use the formula:
Time = Distance / Relative velocity
Given that the cars' front bumpers are initially 100 m apart, we substitute the values into the formula:
Time = 100 m / 5.56 m/s ≈ 18.01 seconds
Therefore, it will take approximately 18.01 seconds for the automobile traveling in the left lane at 60.0 km/h to overtake the car traveling in the right lane at 40.0 km/h when their front bumpers are initially 100 m apart.