If the bus is 100 meters ahead of the car and the bus is travling at 65 km/hr and the car at 78km/hr, how long will it take the car to catch the bus?
I used the following formula, but was informed my answer was wrong.
100m + (t) 65km/hr = 0 + (t)78km/hr
and solved for (t).
t = 100m / (78km/hr - 65km/hr)
I converted km/hr to m/sec and did the math and got
t = 100m / (21.668 m/sec - 18.057 m/sec)
t = 100m / 3.611 m/sec
t = 27.693 seconds
What did I do Wrong?
The only thing I see is significant digits. There is no way you can have the answer in five sig digits, given the input data.
If you leave it in hr, the time for the car to catch the bus is 0.00769 hours.
The bus will travel 0.00769*65 = 0.5 km
The car will travel 0.00769*78 = 0.6 km
The difference is 0.1 km which is the 100 meter separation at th beginning. So the answer MUST be right, at least worked the right way, but the teacher may object to the digits. Perhaps 28 seconds?
Based on the information given, it seems like the approach you used to solve the problem was incorrect. Let's break down the correct approach step by step.
To find the time it takes for the car to catch the bus, we need to consider their relative speeds.
1. Convert the speeds to meters per second (m/s) to have consistent units:
- Bus speed: 65 km/h = (65 km/h) * (1000 m/km) / (3600 s/h) = 18.06 m/s (approximately)
- Car speed: 78 km/h = (78 km/h) * (1000 m/km) / (3600 s/h) = 21.67 m/s (approximately)
2. Set up an equation to represent the situation:
Let t be the time it takes for the car to catch the bus.
The distance traveled by the bus in time t is 100 meters plus (t * bus speed).
The distance traveled by the car in time t is t * car speed.
So, we can write the equation as:
100 + (t * 18.06) = t * 21.67
3. Simplify the equation:
100 + 18.06t = 21.67t
4. Solve for t:
100 = 21.67t - 18.06t
100 = 3.61t
t = 100 / 3.61 ≈ 27.7 seconds
Therefore, the correct answer is approximately 27.7 seconds.
It seems that you may have made a calculation error while converting the speeds to meters per second or in performing the final calculation. Make sure to double-check all calculations to avoid errors.