When Does Runner B Pass Runner A?

[xcompulsion]

Homework Statement

Runner A runs at 6.0m/s for 10s. Runner B accelerates from 4.0 m/s to 10.0 m/s steadily in 10s. How far does Runner A go in 10s? How far does Runner B go in 10s? At what time did Runner B pass Runner A if they were both at the same position at t=0?

Homework Equations

d= v*t, d = 1/2(v1+v2)*t

The Attempt at a Solution

Runner A:
d = v*t
d = (6.0m/s)(10s)
d = 60m

Runner B:
d = 1/2(v1+v2)*t
d = 1/2(4m/s+10m/s)*(10s)
d = 1/2(14m/s)*(10s)
d= 70m

so therefore at 10s, Runner B has already surpassed Runner A by 10m. But how would you find when Runner B passed Runner A?


Many thanks.

 

[Tedjn]

Do you see that you want to find t such that vt = ½(v₁+v₂)t? How can you write v₂ in terms of t?

 

[xcompulsion]

Do you see that you want to find t such that vt = ½(v₁+v₂)t? How can you write v₂ in terms of t?

im sorry. i don't understand..