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Two cars C1 and C2 start their journey from two different points at 4 kmph and 3 kmph respectively and meet after 5 hours at a point where their paths make an angle of 135°. After the cars met, they interchange their paths. Each car first travels to the other car's starting point (i.e. C1 travels to C2's starting point along the path C2 was travelling on and C2 travels to C1's starting point along the path C1 was travelling on ) and then travels along the straight line path (i.e. the shortest distance) joining the starting points of the two cars, finally  reaching  it's original starting point. Find the approximate time interval between the return of C1 and C2  to their starting positions.5-6 hours11-12 hours3-4 hours8-9 hours

Question

Two cars C1 and C2 start their journey from two different points at 4 kmph and 3 kmph respectively and meet after 5 hours at a point where their paths make an angle of 135°. After the cars met, they interchange their paths. Each car first travels to the other car's starting point (i.e. C1 travels to C2's starting point along the path C2 was travelling on and C2 travels to C1's starting point along the path C1 was travelling on ) and then travels along the straight line path (i.e. the shortest distance) joining the starting points of the two cars, finally  reaching  it's original starting point. Find the approximate time interval between the return of C1 and C2  to their starting positions.5-6 hours11-12 hours3-4 hours8-9 hours

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Solution

The problem can be solved in the following steps:

Step 1: Calculate the distance each car traveled before they met. Since they met after 5 hours, car C1 traveled 4 kmph * 5 hours = 20 km and car C2 traveled 3 kmph * 5 hours = 15 km.

Step 2: Calculate the distance between the starting points of the two cars. Since the paths of the two cars make an angle of 135° at the meeting point, the distance between their starting points can be calculated using the law of cosines. The distance is sqrt(20^2 + 15^2 - 22015*cos(135°)) = approx 24.74 km.

Step 3: Calculate the time it takes for each car to travel to the other car's starting point after they met. Car C1 will travel along the path C2 was traveling on, which is 15 km, at a speed of 4 kmph. So, it will take 15 km / 4 kmph = 3.75 hours. Car C2 will travel along the path C1 was traveling on, which is 20 km, at a speed of 3 kmph. So, it will take 20 km / 3 kmph = approx 6.67 hours.

Step 4: Calculate the time it takes for each car to travel along the straight line path joining the starting points of the two cars. Car C1 will travel 24.74 km at a speed of 4 kmph, which will take 24.74 km / 4 kmph = approx 6.19 hours. Car C2 will travel 24.74 km at a speed of 3 kmph, which will take 24.74 km / 3 kmph = approx 8.25 hours.

Step 5: Add up the times for each car to find the total time it takes for each car to return to its starting position. For car C1, the total time is 3.75 hours + 6.19 hours = approx 9.94 hours. For car C2, the total time is 6.67 hours + 8.25 hours = approx 14.92 hours.

Step 6: Calculate the time interval between the return of C1 and C2 to their starting positions. The time interval is 14.92 hours - 9.94 hours = approx 4.98 hours.

So, the approximate time interval between the return of C1 and C2 to their starting positions is between 4 and 5 hours. Therefore, the correct answer is 3-4 hours.

This problem has been solved

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