Rohan, Shikha's boyfriend, had to pick her from her home for a live concert on her 23rd birthday. The venue of the concert and Shikha's home were in opposite directions from Rohan's office. He got late because of some work at office and realised that if he goes to pick Shikha from her home, which was a 48-minute drive from his office, they would be late for the show by 16 minutes. He asked her to start from her home towards his office in an auto-rickshaw and himself started driving towards her home. Both of them started simultaneously, he picked her as soon as they met and they managed to reach the venue just in time for the concert. If Rohan drives at an average speed of 60 km/hr, find the speed (in km/hr) of the auto-rickshaw.
speed time and distance
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So, we know that Rohan would be 16 minutes late if Shikha doesn't leave the house. Therefore, by her leaving they save 16 minutes. the rate that he is going is 60 km/hr so 16 minutes means that by her leaving it reduces the distance Rohan has to travel by 16 km. Since the venue and Shikha house is in opposite direction if she goes 8km towards the office this saves 16 km since Rohan would have had to go 8km there and 8 km back to get the same distance. So we know that the auto rickshaw goes 8km while, Rohan goes 40 km as 8 + 40 = 48km which is the total distance away from the office and hotel since 48 minutes * 60 km/hr is 48km. We know that the rickshaw speed is therefore 1/5 of Rohan speed which is 60/5 = 12 km/hr.