Mechanics Question

From the given values, we can make 2 equations:

Let distance be D and the speed of A be x:

D/(x-30) = 2 OR D = 2 (x-30)
And

D/(2x-30) = 0.4 OR D = 0.4 (2x - 30)

From both the equations above:

2(x-30) = 0.4(2x-30)

or x = 40

so distance between A and B is 20

Please let me know if this is correct ?

N:Dure wrote:??

N:Dure wrote:??

whats the source?

Thanks pesfunk for replying! However I still don't understand how u arrived to the result

Why X-30?

Since both of them were in the same direction, the actual speed should be their difference.

N:Dure wrote:Thanks pesfunk for replying! However I still don't understand how u arrived to the result

Why X-30?

N:Dure wrote:??

simple and plain

Car A >>>>>>> Car B>>>

1st scenario: Car A travels at speed (V1) for 2 hours, Car B travels at speed 30 m/h for 2 hours - Car A catches Car B at point 2 (hours)*V1, the initial distance (D) between both equals to D = 2*V1- 30*2

2nd scenario: Car A travels at speed (V2) for 0.4 hours, Car B travels at speed 30 m/h for 0.4 hours - Car A catches Car B at point 0.4 (hours)*V2, the initial distance (D) between both equals to D = 0.4*V2- 30*0.4

We are given V2=2*V1 (if the speed doubles)

Solve two equations for V1 and V2

D=2*V1- 30*2
D=0.4*V2- 30*0.4

2*V1- 30*2 = 0.4*(2V1)- 30*0.4
1.2*V1=48, V1=40

Find D (distance), D=2*V1- 30*2, D=2*40- 30, D=20

Answer is 20.

p.s. I've tried to simplify as much as possible.

We could plug in the answer choices, which represent the distance between Car A and Car B.

In 2 hours, B travels r*t = 30*2 = 60 miles. In .4 hours, B travels r*t = 30*.4 = 12 miles. When we add these distances to the answer choices, the correct answer will show that if A doubles its rate, it will catch up to B in .4 hours.

Since one of the times given is .4 = 4/10, the correct answer likely will be divisible by 10. Let's skip over answer choice C and try B:

Answer choice B: distance between A and B = 20 miles.
In 2 hours, distance between A and B = 20+60 = 80 miles.
Thus, rate for A to catch up = d/t = 80/2 = 40 miles per hour.
A's rate doubled = 2*40 = 80 miles per hour.
In .4 hours, distance for A = r*t = 80*.4 = 32.
In .4 hours, distance for B = 20+12 = 32. Success!

The correct answer is B.