Normally, we consider speed as distance divided by time, but the distance is assumed to be the same here. So consider this in the form of Y=mX+b where m is tge scale of distance traveled/time and b is used for start day.
A = X/200
B = -x/150 - 30
So you just need to solve for X here:
X/200 = -X/150-30
Math is a language, and you need to translate it in your head to English like any other.
Some simplifying assumptions.
Let the distance from Earth to Mars be equal to 1, and assume it does not change. Let the direction from Earth to Mars be the positive direction.
Assume that the rockets travel at a constant velocity.
The displacement of the rockets can be represented with the lines
S_B(t) = (1/150)(t-30) = (1/150)t - (1/5)
S_A(t) = (-1/200)t + 1
Where t is time in days since rocket A took off. Notice rocket A has a negative slope (negative velocity) since it is moving from Mars to Earth. Rocket A has an initial position of 1, since it starts at Mars. Rocket B has a horizontal shift to the right of 30 days, representing it taking off later.
The rockets cross where these lines intersect. So
(1/150)t - (1/5) = (-1/200)t + 1
((1/150)+(1/200))t = 1 + (1/5)
(7/600)t = (6/5)
t = 720/7 ~= 103
So the rockets cross approximately 103 days after rocket A took off. The position at that time is
S_A(720/7) = (-1/200)(720/7) + 1
=(-18/35) + 1 = 17/35 ~= 0.49
So when they cross, they are about 49% of the way from Earth to Mars. Just closer to Earth than Mars.
When they cross each other, which one is the closet to the earth ?
This is why you read the while question before trying to answer it. When the cross, they are both the same distance from Earth.
Maybe I read it wrong. I don't see how math is necessary at all. If the two ships "cross" each other it means they're at the same point in space right? Or like right next to each other? So they're both the same distance from earth aren't they? Am I about to get woooshed? Lol
Edit: Upon re reading the question I realize it actually says "which one is the closet to Earth."
I'm afraid I don't know the answer to that one...
@[email protected] No you were right at first ! the question is
When they cross each other, which one is the closet to the earth ?
So indeed when they cross they are the same point in space (more or less otherwise it's a collision :) ) so if they are at the same point the are at the same distance to Earth... :)
They’re both the same distance from Earth when they meet.
Ya, more of a logic problem than a math problem based on the question asked
This may not be the simplest, but here's an easy way to just use lots of substitution and basic algebra.
Let t = time in days to meet
Let a = speed (not velocity) of rocket A
Let b = speed (not velocity) of rocket B
1 = 200 * a
1 = 150 * b
200a = 150b
a = (3/4)b
1 = (t * a) + (t - 30) * b
Substitute for a
1 = (3/4)bt + bt - 30b = (7/4)b - 30b
Recall that 1 = 150 * b and set these equal
150b = (7/4 * t - 30) b
Divide by b
150 = 1.75t - 30
1.75t = 180
t ~ 103 days
At 103 days, the ships will meet, and since it's over half the time it takes for rocket A to reach Earth, the meeting point will be closer to Earth.
If I was explaining it to someone, I would get them to figure out the speed as a percentage of the journey.
100/200 = 0.5 per day for A
100/150 = 0.75 per day for B.
Then, I would get them to figure out where A was when B starts the journey.
30*0.5 = 15
So, we care about 85% of the journey.
What else do we know?
We know that the ships get 1.25% of the total distance each day if they are leaving from opposite sides (0.5 + 0.75).
So, that turns this into the question "How many days does it take to go 85 if you are going 1.25 per day? (85/1.25)"
Not a bad approach, but 100/150 is 0.6666, not 0.75.