SOLUTION: Cars A and B travel down the same road. A's speed is r km/h and B's speed is s km/h (A's speed is less than B's) When will B overtake A? t=A's time. 1. A and B start at the

Algebra ->  Equations -> SOLUTION: Cars A and B travel down the same road. A's speed is r km/h and B's speed is s km/h (A's speed is less than B's) When will B overtake A? t=A's time. 1. A and B start at the       Log On


   



Question 873552: Cars A and B travel down the same road. A's speed
is r km/h and B's speed is s km/h (A's speed is less than B's)
When will B overtake A? t=A's time.
1. A and B start at the same time but A starts p km in front of B.
2. A and B start in the same place but A starts q hours before B.
Thank you.

Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
r%3Cs
t = UNKNOWN time
r = speed of carA
s = speed of carB
Conditions Number 1: Same departure location, A starts p kilom ahead of B.
This means car A is starting at a position p, and while traveling, position becomes p+rt.

Basic Rule: RT=D for rate, time, distance.

WHICH CAR___________Speed________time_______distance
A___________________r____________t__________p+rt
B___________________s____________t___________st

The variable t is to be the same value for when B overtakes A and is unknown. The distance expressions must be equal when B overtakes A, and this equality uses only the unknown of t.

highlight%28p%2Brt=st%29;
Solve for t, the only unknown variable.
st-rt=p
%28s-r%29t=p
highlight_green%28highlight%28t=p%2F%28s-r%29%29%29