the distance between town A and town B was 210km. At 9:20pm a bus sets off from town A to town B and a car left from town B to town A. The average speed of the bus was 60km/h and the average speed of the car was 80km/h.
a)Calculate the time at which the car passed the bus.
b)How far had the car traveled when it passed the bus?
they both drove the same time, t hrs
so 60t + 80t = 210
140t = 210
t = 210/140 = 1.5
after 1.5 hrs, they met.
and that time was 9:20 + 1:30 = 10:50 pm
distance traveled by car = 1.5(80) = 120 km
To solve this problem, we need to consider that the distance between town A and town B is 210km. The bus is traveling at an average speed of 60km/h and the car is traveling at an average speed of 80km/h.
a) To calculate the time at which the car passed the bus, we need to determine the time it takes for each vehicle to travel the distance.
Let's assume that the car and the bus meet at time t hours after they start traveling. At t hours, the bus will have traveled a distance of 60t km, and the car will have traveled a distance of 80t km.
Since the total distance between town A and town B is 210km, we can write the equation:
60t + 80t = 210
Combining like terms:
140t = 210
Dividing both sides by 140:
t = 1.5 hours
Therefore, the car will pass the bus 1.5 hours after they start traveling, or at 9:20 pm + 1.5 hours = 10:50 pm.
b) To calculate the distance the car has traveled when it passes the bus, we can substitute the value of t into either the car's distance equation or the bus's distance equation.
Using the car's distance equation:
Distance = 80t = 80 * 1.5 = 120 km
Therefore, the car will have traveled 120 km when it passes the bus.
To answer these questions, we can use the formula Distance = Speed * Time.
a) Calculate the time at which the car passed the bus:
Let's assume that the car passed the bus after a time of t hours.
Distance covered by the bus = Speed * Time
Distance covered by the car = Speed * Time
As per the given information,
Distance covered by the bus = 60 km/h * t
Distance covered by the car = 80 km/h * t
Since the total distance between the two towns is 210 km, we can write the equation:
60 km/h * t + 80 km/h * t = 210 km
Simplifying the equation:
140t = 210
Solving for t:
t = 210 / 140
t = 1.5 hours
Therefore, the car passed the bus after 1.5 hours, or 1 hour and 30 minutes.
b) How far had the car traveled when it passed the bus:
To calculate the distance traveled by the car when it passed the bus, we can substitute the value of t into either of the distance equations.
Using the equation "Distance covered by the car = 80 km/h * t":
Distance covered by the car = 80 km/h * 1.5 hours
Distance covered by the car = 120 km
Therefore, the car had traveled 120 km when it passed the bus.