Two cars started from the same point and traveled on a straight course in opposite directions..........?

Question

exactly two hours at which time they were 208 miles apart. If one traveled on average 8mph faster than the other car. What was the average speed for each car, for the two hour trip?

What formula do you use? A full explanation would be helpful. Thank you!

Answer 1

Let x = speed of 1st car, x + 8 mph = speed of the other car.

Determine speed of 1st car:
2 hours (x + x + 8 mph) = 208 miles
2 hours (2x + 8 mph) = 208 miles
4x + 16 miles = 208 miles
4x = 192 miles
x = 192 miles / 4 hours
x = 48 mph

Determine speed of the other car (substitute x with 48):
= x + 8 mph
= 48 mph + 8 mph
= 56 mph

Answer: speed of :1st car is 48 mph; the other is 56 mph

Proof (total distance covered by 2 cars):
= 2 hours (48 mph) + 2 hours(56 mph)
= 96 miles + 112 miles
= 208 miles

Answer 2

Let v mph be the average speed of the slower car, then
v + 8 mph is the speed of the faster car.
In 1 hour, they are v + v + 8 = 2v+8 miles apart.
In 2 hours, there are 2 (2v + 8) = 208 miles apart
4v + 16 = 208
4v = 208 - 16 = 192
v = 48

average speed of slower car = 48 mph
that of faster car = v + 8 = 56 mph

Answer 3

Remember that speed is distance divided by time, so since s = d/t then s*t = d (distance is speed times time).

We don't know the speed of one car, but we know the other car's speed is 8 mph more than it, so call the two car speeds s and s+8. They were both traveling for 2 hours, so the first car must have gone a distance of 2s and the second a distance of 2(s+8).

Finally, we know that their combined distances from the starting point is the same as the distance between the two cars at this time, so add up the two distances and set it equal to 208
s + 2(s+8) = 208

Now solve this for s. That gives you the speed of one car. Remember the other car's speed is just 8 more than this.

Answer 4

they traveled a total of 208 miles in 2 hours, which make the total of their 2 speeds = 104 mph
one car 's speed is (lets call it "S") and the other one is 8mph faster so the formula would be...
S + (S + 8) = 104
2S = 104 - 8
S = 96/2
S= 48 and the other car speed is 56
so its 48mph and 56 mph

Answer 5

You should avoid special formulas for each type of problem. The general one for this type of problem is
DISTANCE APART= Sum(velocity* time)
Here let Car 1 travel in one direction at X mph
Let Car 2 travel in the other direction at X+8 mph.
Then 208 = 2X + 2(X+8)
So 192= 4X and X = 48 mph.

Answer 6

OK here is what I see two cars went 208 miles in 2 hrs or 104 miles in 1 hrs s1 + s2 x 1 hr = 104 miles one went 8 miles faster s1+ S2+8=104
LET SIMPLIFY by collecting terms
S1+S2=2S and 104-8=96
2S=96
S =48
S+8 =56
the two cars speeds are 48mph and 56mph
checking we find:
56+56 +48+48=208MILES

THERE IS no formula you just use the sentence structure to formulate an equation of what it says...then check to make sure your OK...Hope that helps a little....From the E..

Answer 7

let the speeds be a mph and (a+8) mph giving
rate separating x time = separation
( a + a + 8) m/h x 2h = 208m
=> 4a + 16 = 208
=> 4a = 192
=> a = 48 and a + 8 = 48 + 8 = 56
speeds were 48 mph and 56 mph.

Answer 8

you gotta just throw a formula together: you figure distance is equal to time times speed, and while you don't have the actual speed you know how they differ, and can substitute a variable in for it. so lets have speed equal x: 208 = [2 times x] + [2 times (x+8)] when you solve the equation for X, you should have the speed of the one car and when you multiply that by 8, you should have the speed of the other car

Answer 9

Let S be the speed of one car. The speed of the other car is
S + 8 . Right?
Distance travelled by the first car in 2 hours = 2S.
-----------------------------second car ----------- 2( S + 8 ) = 2S + 16
Now, 2S + 2S + 16 = 4S + 16 = 208 or 4S = 192 or
S = 48 mph; the other car = 56 mph. Is it clear?

Answer 10

we can solve this problem by two methods,let Va=V+8 ,Vb=V
1) 2(V+8) +2V = 208 then V= 48 mil/h and V+8 = 56mile/h

2) using relative velocity Va→b= Va -Vb= V+8-(-V) as in opp.direction .
then Va→b= 2V+8 , THEN 2(2V+8)= 208
then V= 48 mil/h and V+8 = 56mile/h