In a 100 metre race, A can allow B to start the race either 10 metres ahead of the starting point or 2 seconds before A so that both reach the finishing line at the same time. What is the speed of B in m/sec and how long will A take to run 100 m? Choose the correct choice from the following answers: A) 6 m/sec; 18 sec B) 5 m/s; 18 sec C) 4 m/s; 15 sec D) 3 m/s; 12 secs E) 2 m/s; 6 secs
A can allow B to start the race 10 metres ahead, so the time A need to cover 100 meters equals to the time B needs to cover 90 meters --&gt; 100/a = 90/b, where a and b are the rates of A and B, respectively.   A can allow B to start the race 2 seconds before A, so the time A need to cover 100 meters is 2 seconds less than the time B needs to cover 100 meters --&gt; 100/a + 2 = 100/b.   Subtract one from another: 2 = 100/b - 90/b --&gt; b = 5.   Answer: B.   Or directly: 5 m/s; 18 sec needs 2 seconds more to cover 100 meters than to cover 90 meters --&gt; 2 = 100/b - 90/b --&gt; b = 5.
<result>B</result>
In a 100 metre race, A can allow B to start the race either 10 metres ahead of the starting point or 2 seconds before A so that both reach the finishing line at the same time. What is the speed of B in m/sec and how long will A take to run 100 m?