The distance from the railway station to a village is four kilometres. A boy and a car left the station at the same time for village. Ten minutes later, the boy met the car on its way back from the village. After he had walked another 1/14 km, he met the car once again which drove to the station and was headed back for the village. Find the respective speeds (in km/hr) of the boy and the car, assuming them to be uniform with no stoppages.

The boy walks at a constant speed while the car makes continuous trips between the station and the village. In the first 10 minutes, the boy walks (10 multiplied by v_boy) divided by 60 km while the car travels to the 4 km village marker and returns, meaning their combined distance equals 8 km; this gives the equation (v_boy plus v_car) multiplied by (1 divided by 6) equals 8, so v_boy plus v_car equals 48. The boy then walks an additional 1/14 km, taking (1 divided by 14) divided by v_boy hours, during which the car returns to the station and comes back to meet him; the car's total travel distance of 4 km plus its position relative to the station equals its speed multiplied by that time. Testing the option where the boy walks at 3 km/hr, the 1/14 km walk takes 1/42 hours, during which the car travels 45 multiplied by 1/42, totaling 15/14 km; since the car travels from the 4 km village marker back to the station and then out again for 1/14 km, its position perfectly matches the boy's 1/14 km distance from the station. Therefore, the respective speeds are 3 km/hr for the boy and 45 km/hr for the car.

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