Question

How do i go about this rational expression problem?

Bob and Jack enter a 1000-km bicycle race. Bob cycles 4 km/h faster than Jack, but his bicycle gets a flat tire, which takes 30 minutes to repair. If the both of them finish the race in a tie, then how fast was each boy cycling?
Give your answer in one decimal place.

Answer 1

assume the velocity for jack=v
then velocity for bob=v+4
total time for bob=\[[1000/(4+v)]+0.5\]
it has to equal to time for jack=\[1000/v\]
after solving the 2 equition, we got v=87.465, and v+4=91.465
for only one decimal
v=jack=87.5 km/h
v+4=bob=91.5 km/h

Answer 2

How would i go about actually solving that equation though?

Answer 3

\[[1000/(4+v)]+0.5=1000/v\]
\[(1000+2+0.5v)/(4+v)=1000/v\]
times the button to the other side
\[1002v+0.5v^2=4000+1000v\]\[0.5v^2+2v-4000=0\]
use the formula
v=
\[[-b+\sqrt{b^2-4ac}]/2a\]