SOLUTION: The distance between town P and Q was 540 km. A car started from town P travelling at a speed of 100km/h towards town Q.At the same time,a van started from town Q travelling towar

Algebra ->  Finance -> SOLUTION: The distance between town P and Q was 540 km. A car started from town P travelling at a speed of 100km/h towards town Q.At the same time,a van started from town Q travelling towar      Log On


   

Question 1163874: The distance between town P and Q was 540 km. A car started from town P travelling at a speed of 100km/h towards town Q.At the same time,a van started from town Q travelling towards town P at a speed of 80 km/h. Find the distance travelled by the car when they pass each other.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Car 1 starts at point P and goes 100 km/h toward town Q. The distance traveled here is
d = r*t
d = 100t

Car 2 will travel a distance of
d = r*t
d = 80t
for similar reasoning, just with a different speed value of course.

Together the two distance expressions add to 100t+80t = 180t to represent the total distance traveled. When the two cars meet, this total distance must be 540

I recommend drawing a number line to plot P and Q at the endpoints. Somewhere in between those endpoints, plot point R. Point R is where the two cars meet. Segment PR has a distance of 100t while QR is of length 80t. The total is 180t as found above and this total must be equal to PR = 540.

So our equation to solve is
180t = 540
which becomes
t = 3
after dividing both sides by 180

The last step is to plug this t value into each distance expression
100t = 100*3 = 300 is the distance car 1 travels
80t = 80*3 = 240 is the distance car 2 travels

Answers:
The car starting at point P traveled 300 miles
The car starting at point Q traveled 240 miles