A train is moving with constant speed of 5m/s and there are 2 persons A and B standing at a separation of 10m inside train. Another person C is standing on the ground . A moves towards B and back to its position in 10 seconds with constant speed. Then, distance covered by A , in frame of reference of C, is?

A and B are separated by the distance of 10 m. A moves toward B and returns to its position (that is 10 m away from B) with a constant speed in 10 s. Then the distance covered in 10 s is 20 m. Then the speed of A is 2 m/s. For constant speed, A will take 5 s to reach B & then another 5 s to get back at its position. For the first 5 s, velocity of A will be 5+2=7 m/s towards the direction of train`s velocity with respect to C as the train velocity is 5m/s. So the distance covered at first 5 sec will be 35 m. Similarly for the last 5 s, resultant velocity of A will be 5-2=3 m/s towards the velocity of train and so covered distance will be 15 m/s. So the total distance covered by A with respect to C will be 50 m. Check if it is the answer given. If not, inform me, I`ve another concept to solve it which a little more complex.