Physics problem-please help?

Question

I'm working on my GRE's and I 'm really stuck here. Looks like it should be easy but I can't figure it out.

Two cars start 0 distance apart and travel in opposite directions. After two hours, they end up 208 miles apart. What is the average velocity for each car if one of them has traveled with an average velocity 8mi/h faster than the other?

Answer 1

(x mph * 2 hours) + ((x+8) * 2 hours)= 208
2x + 16 + 2x = 208
4x = 192
x= 48 mph

the average speed is then (48) + (48+8)/2
or 52 mph

Answer 2

Let the average speed of one car be v and the other car be v'. You have to solve two equations.

First, the equation relating the two speeds is v = v' + 8.

The second equation says that the sum of the distance (you don't need to worry about relative velocity because the cars start in the same place) travelled by the two cars is 208 miles. In math, this becomes vt + v't = 208, where t = 2 (hours).

Substituting v = v' + 8 and t = 2 into the second equation:

2v' + 8*2 + 2v' = 208
4v' = 208 - 16
v' = 48

Substitute v' = 48 back into v = v' + 8 to get v = 56.

Therefore, one car has an average speed of 48 mi/h and the other car must have an average speed of 56 mi/h. Now to turn the speeds into velocities, just say that the cars are moving in opposite directions.

Answer 3

Average velocity? Well on average each car has travelled 208/2=104 miles in 2 hours. So the average velocity is 104/2=52mph. That's a quicker answer than some of the others. One car going 8mph faster than the other is not actually important if you only want to find the average velocity.

Answer 4

Both start from the same point, and travel till they are 208 mi apart. Therefore both cars travel 104 mi (1/2 of 208).

What speed must a car go at to travel 104 mi in 2 hours.
v=d/t
v=104/2
v=52mph

Assuming both cars completed the journeys at the same spped, the would travel at 52mph. But your question has a twist. One car is going 8mph faster than the other.

If we add on 8 to 52, we get 60. Put this in to the v=d/t and add it to the other car:
Car 1: v=d/t, d=vt, d=60x2=120 miles travelled
Car 2: v=d/t, d=vt, d=52x2=104 miles
Distance apart is 224. So that can not be right.

If we deduct 8 from 52, we get 44. Put this in to the v=d/t and add it to the other car:
Car 1: v=d/t, d=vt, d=44x2=88 miles travelled
Car 2: v=d/t, d=vt, d=52x2=104 miles
Distance apart is 192. So that can not be right.

You have probably spotted it by now, if not, I'll check back to this Q later to finish.

Answer 5

Let x = car1 mph
Let (x+8) = car2 mph

After 2 hours, they are 208 miles apart, so they travelled 104 miles/hour.

x + (x+8) = 104 mph
x + x + 8 = 104 mph
x + x = 104 - 8 mph
2x = 96 mph
x = 48 mph (car1)
x + 8 mph = 56 mph (car2)

Boris got it right. I think Lexie meant "56 mph" instead of "52 mph" (52 mph would make the average velocity only 4 mph more than the other car)

You can check. After one hour, one car has gone 48 miles one way, the other car went 56 miles the other way, totalling 104 miles apart. After two hours, they will wbe 208 miles apart (104 miles x 2).

Answer 6

Cars are speeding apart at rate of x + y miles/hr where x is lower speed and y is higher speed, which is also x+8 miles/hr. So -
cars speeding apart at x + (x+8) miles/hr
after 2 hours, cars are 208 miles apart, so -
2(x + x+8) = 208, so 2x + 2x +16 = 208
so 4x + 16 = 208, so 4x = 208 - 16, so 4x = 192, so x = 192/4
x = 48 miles/hr, y = x + 8 = 56 miles/hr (ANSWER)
In 2 hrs car x travels 96 miles and car y travels 112 miles, a total of 208 miles. QED

Answer 7

AV = average velocity = change in distance / change in time

AV1 = x [miles] / 2 [hours]
AV2 = (208 - x) [miles] / 2 [hours]

But, AV1 = AV2 + 8 [mi/h]

x/2 = (208 - x)/2 + 8
x = (208 - x) + 16
2x = 224

x = 112 miles
(208 - x) = 96 miles

AV1 = x [miles] / 2 [hours] = 56 mi/h
AV2 = (208 - x) [miles] / 2 [hours] = 48 mi/h

Answer 8

if x is the velocity of the slowest,

then x + (x + 8) = 208/2

so 2x = 104 - 8

x = 48 so the other is 56

Answer 9

One car travels at 48mph and the other at 56mph on average.

One car travels a total of 112 miles, and the other 96.

Knowing the answer does not help you solve the problem, you have to do it yourself first.

Answer 10

Let the speed of car A be Xmph, and the speed of car B be (X+8)mph. Total speed of divergence = (2X+8)mph

Take it from there.