Simple algebra II question. Can't think of the answer.?

Question

I'm pretty embarrassed about not knowing the answer to this right off the bat. But it is the first day of school, so I suppose this is forgivable. Anyway:
Two cars leave Springfield at noon and travel in opposite directions. If one car travels r mi/h and the other travels 1.5 times as fast, how far apart are the cars at 4:00 p.m.? Give the answer in simplest form in terms of r.
Please help me and explain how this is done so I will have something to base further studies of distance problems off of. Thank you.

Answer 1

Donot worry Dave.It is simple arithmatic.When two cars travel in the opposite directions their resultant speed or relative speed is the sum of their respective speeds
Here one car has a speed of r mi/h and as indicated the second car's speed is 1.5 times of r which 1.5r
Therefore,their relative speed is r+1.5r=2.5r
So in 4 hours they will be 4*2.5r or 10r miles away from each other

Answer 2

This is quite straightforward.

The cars start at noon and travel for 4 hours
1 car drives at r mph and the other 1.5 times as fast so after 4 hours car 1 has travelled 4 x r, Car 2 has traveled 1.5 times as far so = 4 x 1.5r = 6r. The cars are, therefore, 4r + 6r apart = 10r

If r = 30 mph then after 4 hours car 1 would have travelled 4 x 30 =120 miles. Car 2 would have travelled (4 x 30) x 1.5 = 180 miles. Add the two together and it's 120 + 180 = 300

Answer 3

First 12:00 to 4:00 is 4 hours.
car one travels r mph
car two travels 1.5r mph
d is distance apart:
the distance they are going to be separating at any given time is
r+1.5r
the distance they are going to be apart after 4 hours will be 4 times the distance they are separating and any given instant in time:

4(r+1.5r) = d
now if you want to get real fancy: you can factor out r:

4r(1 +1.5) =d
4r(2.5) =d
10r = d
where d = total distance apart. and r = rate of travel.

You can also write this in a general formula form if no values are given.
you can let t = the time travelled
and you can let x = the different between the speed of the first car and second car.

doing it that way you have.
t(r + xr) =d
factoring out rate gives you
t*r*x =d
where t = time
where r = rate
where x = difference in rate
where d = distance.
That help any?

Answer 4

Distance is defined in this problen as d= rate/time
First car leaves spring field at 12:00 pm at a rate of speed r and travels for 4:00 hours.. The second car travels in the opposite direction at at a rate of seed 1.5 time faster and also travels for 4:00. We want to solve for r.
d=r/t
Mutiply both sides of the equation by T(time)
dt=r
r=dt

r=d multiplied by 4hrs for the first car

1.5r=d multiplied by 4 hours by the second car

To solve for distance apart in terms of r we add1and1.5 to give us the distance apart. this is 2.5

We return to our equation r=dt

r=2.5 multiplied by time wich is 4 hours

r=10 hours apart

Answer 5

1.5r mi/hr r mi/hr
car1 <-------------------------|---------------------> car2
4hrs x 4 hrs

x = is the point of origin
time(1) = 4hours
time(2) = 4 hours
velocity of car1 = 1.5r
velocity of car2 = r

distance (d) = velocity( v) x time (t)

distance(1) = (1.5r)(4) = 60r miles
distance(2) = (r)(4) = 4r miles

it means if we will set a velocity(r) of 10 mi/hr it means that car 1 is 600miles away from the origin, and car2 is 40miles away from the origin.

If that's the case then the distance of car1 to car2 is just the sum of their distance with respect to the origin.

distance of the car1 to car 2 is equals 60r plus 4r which is 64r

Or in the example i stated the cars would be 640miles apart