Two cars started at sunrise and travelled at a constant speed,one from city A to city B and the other from city B to city A on the same highway.They met at noon and without stopping and arrived respectively at city B at 4 p.m. and at A at 9 p.m.
required:determine the sunrise time for that required:determine
(10 marks)
To determine the sunrise time, we need to calculate the total travel time for each car.
Let's assume that the distance between city A and city B is d, and the speed of the car traveling from city A to city B is v1, and the speed of the car traveling from city B to city A is v2.
Since both cars started at sunrise and met at noon, the total travel time for each car can be calculated as follows:
Total travel time for car traveling from city A to city B = Time it took for the cars to meet + Time it took for the car to travel from the meeting point to city B
Total travel time for car traveling from city B to city A = Time it took for the cars to meet + Time it took for the car to travel from the meeting point to city A
Given that the car traveling from city A to city B arrived at city B at 4 p.m., we can write the equation as:
Total travel time for car traveling from city A to city B = 4 p.m. - 12 p.m. = 4 hours
Similarly, given that the car traveling from city B to city A arrived at city A at 9 p.m., we can write the equation as:
Total travel time for car traveling from city B to city A = 9 p.m. - 12 p.m. = 9 hours
Now, let's consider the meeting point. Since both cars traveled at a constant speed, the distance traveled by the car traveling from city A to city B is the same as the distance traveled by the car traveling from city B to city A. Therefore, we can write the equation as:
Distance traveled by car traveling from city A to city B = Distance traveled by car traveling from city B to city A = d
Now, let's calculate the speeds of the cars:
Speed of car traveling from city A to city B = v1
Speed of car traveling from city B to city A = v2
Since we know that the total travel time for each car can be calculated as:
Total travel time for car traveling from city A to city B = Distance traveled by car traveling from city A to city B / Speed of car traveling from city A to city B
Total travel time for car traveling from city B to city A = Distance traveled by car traveling from city B to city A / Speed of car traveling from city B to city A
We can substitute the known values into the equations:
4 hours = d / v1
9 hours = d / v2
Now, we have two equations with two unknowns (d and v). We can solve these equations simultaneously to find the values of d and v. The values of d and v will depend on the specific values given in the problem.