Final answer:
Hirendra and his wife have a combined speed of 9 km/h while moving towards each other from a distance of 81 km apart. It takes them 9 hours to meet. Therefore, Hirendra's wife, who is walking at a speed of 3 km/h, will cover a distance of 27 kilometers to meet Hirendra.
Step-by-step explanation:
The question involves calculating the distance Hirendra's wife will have traveled when they meet, given that Hirendra and his wife start at a distance of 81 km apart and move towards each other, with Hirendra walking at 6 km per hour and his wife walking at 3 km per hour. To solve this, we can set up a relative speed equation because they are moving towards each other. The combined speed of Hirendra and his wife is the sum of their individual speeds.
The total distance between them is 81 km. Their combined speed is 6 km/h + 3 km/h = 9 km/h. The time taken for them to meet can be calculated by dividing the total distance by their combined speed.
Time taken to meet = Total Distance / Combined Speed = 81 km / 9 km/h = 9 hours.
Since Hirendra's wife is walking at 3 km/h, we multiply the time taken by her speed to get the distance she covers.
Distance covered by Hirendra's wife = Speed of wife × Time taken to meet = 3 km/h × 9 hours = 27 km.
Therefore, Hirendra's wife will have to commute 27 kilometers when they meet.