October 2013



Sample Analysis at Mars Science: Data from NASA's Curiosity rover has revealed the Martian environment lacks methane. This is a surprise to researchers because previous data reported by US and international scientists indicated positive detections. Read more ....

Brain image If you got beat up by a bully on your walk home from school every day, you would probably become very afraid of the spot where you usually met him. However, if the bully moved out of town, you would gradually cease to fear that area. Read more ....

Galaxy picture Astronomers using NASA's Hubble Space Telescope and Chandra X-ray Observatory and telescopes on the ground may have found the most crowded galaxy in our part of the universe. Read more .....

Nanoparticles image Many viruses and bacteria infect humans through mucosal surfaces, such as those in the lungs, gastrointestinal tract and reproductive tract. To help fight these pathogens, scientists are working on vaccines that can establish a front line of defense at mucosal surfaces. Read more ....

Space weather effects on satellites Is your cable television on the fritz? One explanation, scientists suspect, may be the weather - the weather in space, that is. Read more ....

Cheetahs A study by University of Georgia ecologists has found that diversity in mammal immune system genes may have more to do with the opportunity to choose a mate than with exposure to parasites. Read more ....

Locked door Humour: Locked out of your own house can be an alarming eperience, especially if you are new to the neighbourhood where neighbours are yet to make your acquaintance. I should know because I have gone through that embarrassing situation. Read more ....




Solution

My friend and I are walking towards each other because it is a circular track. Right. When we are walking towards each other, the speeds get added. For instance, if my speed is 2 kilometres per hour and my friend's speed is 3 kilometres per hour, then in one hour we, together, cover a distance of 5 kilometres. That is the case here too. Our speeds are in the ratio 2:3, so our collective relative speed is 2+3 = 5 rounds per hour. So in one hour, we together make five rounds of the track and, therefore, cross each other five times. In 30 minutes, we make two rounds and so cross each other twice. Therefore, in one-and-half hours we cross each other seven times.

Pie diagram Now if I really want to know when we cross each other, I prefer to draw a pie. I find this convenient. It helps me to keep track of things, while keeping in mind that distance = speed x time. So everytime I need to find the time, I draw a pie and after substituting the values for distance and speed, I find the time.

Since the speeds have been given as a ratio and no actual distance has been mentioned, I think I can conveniently assume a distance. It doesn't matter because the speeds will work out accordingly.

Let me assume that the circumference of the circular track is 600 metres. Then my speed is 1200 metres per hour (I make two rounds per hour) and my friend's speed is 1800 metres (he makes three rounds per hour).

So our collective speed is 1200 + 1800 = 3000 metres per hour. We will first meet when together we have covered 600 metres. Therefore, distance = 600 and speed = 3000 metres per hour. Now distance = speed x time, so 600 = 3000 x t1. Thus, t1 = 1/5 hours, or 12 minutes. So after we start walking, we will meet for the first time after 12 minutes. Having crossed each other, we will meet again after covering another 600 metres. So for the second meeting, the total distance covered is 1200 metres. Distance = speed x time, so 1200 = 3000 x t2. Therefore t2 = 2/5 hours, or 24 minutes.

The third meeting will occur after covering 1800 metres, after 36 minutes. The fourth will occur on covering 2400 metres, after 48 minutes. This is how it goes.

Thus, if we keep walking, we will meet after 12, 24, 36, 48, 60, 72, 84, 96, 108, ...... minutes. But we have walked for one-and-half hours, that is 90 minutes. So, during this 90 minutes we have crossed each other for the last time at the 84th minute. We have crossed each other seven times - at the 12th minute, 24th minute, 36th minute, 48th minute, 60th minute, 72nd minute and 84th minute.



Some useful links for
your career:


  • Union Public Service Commission - www.upsc.gov.in
  • IIT-Kharagpur - www.iitkgp.ac.in
  • Indian Statistical Institute - www.isical.ac.in
  • Indian Institute of Technology Madras - www.iitm.ac.in
  • Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
  • Indian Institute of Mass Commission - www.iimc.nic.in
  • IIT Bombay - www.iitb.ac.in
  • Indian School of Mines, Dhanbad - www.ismdhanbad.ac.in
  • Birla Institute of Technology, Ranchi - www.bitmesra.ac.in
  • Central Institute of Fisheries Nautical and Engineering Training - www.cifnet.nic.in
  • Indian Institute of Information Technology, Allahabad (Deemed University) - www.iiita.ac.in
  • Central Marine Fisheries Research Institute, Kochi - www.cmfri.com
  • Tata Institute of Social Sciences, Mumbai - www.tiss.edu