A car trveling at 88km/h. If the bus has a 1.5h head start, how far from the starting point does the car overtake the bus?
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A car trveling at 88km/h overtakes a bus trveling at 64kmlh. If the bus has a 1.5h head start, how far from the starting point does the car overtake the bus?
At the moment the car overtakes the bus,
the bus has gone D/64 hrs
the car has gone D/88 hours
Isn't the time of the bus 1.5 hours more than the car?
Take it from there
To find out how far from the starting point the car overtakes the bus, we need to determine the time it takes for the car to catch up to the bus.
Let's assume that the distance from the starting point to the point where the car overtakes the bus is D, and the time it takes for the car to catch up to the bus is T.
We know that the car's speed is 88 km/h. Since speed is defined as distance divided by time, we can use the formula speed = distance / time to solve for the time it takes for the car to reach the bus.
Now, let's calculate the time it takes for the car to reach the bus:
The bus has a head start of 1.5 hours, so by the time the car starts, the bus has already traveled a certain distance. Since we don't know the exact distance the bus has traveled during that time, we can calculate it by using the formula distance = speed * time.
Given that the bus's speed is 0 km/h (since the bus is stationary during the head start), and the time is 1.5 hours, we can calculate the distance traveled by the bus as follows:
Distance = Speed * Time
Distance = 0 km/h * 1.5 hours
Distance = 0 km
Therefore, the bus has traveled 0 km during the 1.5-hour head start.
Now, let's determine the time it takes for the car to catch up to the bus:
Distance = Speed * Time
D = 88 km/h * T
Since the car starts from the same point as the bus (when the head start is already completed), the distance the car has traveled will be equal to the distance the bus has traveled plus the distance from the starting point to the point of overtaking, which is D.
Distance car = Distance bus + D
Distance car = Speed bus * Time + D
But we know that the speed of the bus is 0 km/h (since the bus is stationary during the head start), and the time it takes for both the car and bus to reach the point where the car overtakes the bus is T. So, we can rewrite the equation as:
D = 0 km/h * T + D
D = D
Now, we can solve for T:
D = 88 km/h * T
Dividing both sides by 88 km/h:
D / 88 km/h = T
So, the time it takes for the car to catch up to the bus is T = D / 88 km/h.
Therefore, the car overtakes the bus a distance of D from the starting point after a time of D / 88 km/h.