Runner A & B Race: Find Out When & How Far!

[phywhat]

Help with homework??

Runner A, who runs with an average speed of 3.0 m/s, starts out at 3:00 P.M. Runner B, who runs with an average speed of 4.0 m/s, starts after A from the same place exactly 5 min later.
a.) At what time will runner B catch up with runner A?
b.) If the runners stop when B catches A, how far do they run?

 

[needhelpperson]

this should go in the homework section... as well... you should show some work first, otherwise ppl are not going to help you.

 

[jdstokes]

Runner A, who runs with an average speed of 3.0 m/s, starts out at 3:00 P.M. Runner B, who runs with an average speed of 4.0 m/s, starts after A from the same place exactly 5 min later.
a.) At what time will runner B catch up with runner A?
b.) If the runners stop when B catches A, how far do they run?

You know $v_A = 3$ and $v_B = 4$ Integrating with respect to time gives $x_A = 3t + C_A$ and $x_B = 4t + C_B$. When $t=0$, $x_A = 0$ so $x_A = 3t$. When $t=300$, $x_B = 0$, so $x_B = 4t - 1200$. Runner B catches runner A when $x_A=x_B$. That should be all you need to know.