Math Distance Question. Where Would Two Trains Meet Going To And From The Same City

Distance/speed and Time Math question?

I need help with these 2 questions.
1. The tape moves at 2 cm per second on a certain tape recorder. An M30 tape will record 15 minutes on each side. How long in centimeters is an M30 tape?

2. Non stop trains leave Toronto and Montreal at the same time each day going to the other city along the main line. One train travels at 120km/hr and the other at 90 km/hr. Assuming the track is straight, how far apart are they one hour before they meet?

Math word problems Two trains distances arrival time?

Math word problems Two trains distances arrival time?

Kayla

Two trains are traveling on the same route and leave their respective stations at same time. The one going west averages a speed of 60 mph and makes a stop for one quarter of an hour. The one traveling east is traveling at an average speed of 45 mph. Distance between the stations is 1050 miles. ASt what distance from each station do they meet?

let m = distance of the train traveling at 45 mph to the meeting point
D = 1050 mi
T(45) = time traveled by the train at 45 mph to the meeting point
Time = Distance / Speed
T(45) = m/45

T(60) = time traveled by the train at 60 mph to the meeting point
T(60) = (D - m) /60
T(60) = (1050 - m) /60

Total time to accomplished the meeting = T(45) + (T(60) - 1/4)

Total time equivalent = D / 45 + 60
Total time equivalent = 1050 / 45 + 60
Total time equivalent = 10 hrs

Total time equivalent = Total time to accomplished in meeting
Total time to accomplished the meeting = T(45) + [(T(60) - 1/4)]
10 = m/45 + [(D - m)/60 - 1/4)]
10 = m/45 + [(1050 - m)/60 - 1/4)]
10 = m/45 + [4(1050 - 4m) - 60)]
70 = m + 45(4)(1050) - (45)16m

m = 258.5 miles

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Base on the train traveling at 45 mph going east they meet at 258.5 miles

Base on the train traveling at 60 mph going west they meet at 1050 - 258.5 miles
or
Base on the train traveling at 60 mph going west they meet at 791.5 miles
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hope this helps
Remember that Jesus loves you. Know Him in His words the bible.
God Bless

Mental Math question?

Non stop trains leave Toronto and Montreal at the same time each day going to the other city along the main line. One train travels at 120km/hr and the other at 90 km/hr. Assuming the track is straight, how far apart are they one hour before they meet?

This is the only information I have on this question.

Math question?

I have no idea why this question is in the Religion section.

So I will reply with an answer that does belong here.

Islam and Christianity, the "daughter" religions of Judaism, have hundreds and thousands of years of war and suppression to their names. The original, Judaism, is peaceful and never made a religious war on those who believe differently.

You have, of course, the Crusades as the prime example.

The reason for the conflict between Israel and the Arabs is that the Arabs, plain and simple, refuse to accept a Jewish state in their midst. They invented this whole idea of a "Palestinian people who deserve a state" just to use as a tool to dismember Israel.

Arab violence against Jews has been going on long before there was an occupation, long before there was a refugee problem--indeed, long before there was a political Zionist movement. Need I present more painful examples? Perhaps even further back, where I hope everyone will agree that the Zionist movement did not yet come into being:

In the centuries after Muhammad there have been periods when the Jews were able to live in relative peace under Arabs, but their position was never secure. They were generally viewed with contempt by their Arab neighbors, and their survival was always predicated on their abject subordination and degradation to them. Mass murders of Jewish "protected people" started in Morocco as early as the eighth century, where Idris I wiped out whole communities. A century later Baghdad's Caliph al-Mutawakkil designated a yellow badge for Jews (setting a precedent that would be followed centuries later in Nazi Germany), and synagogues were destroyed throughout Mesopotamia in 854-859. In Tripolitania, Jews were considered the property of their Arab masters, who would bequeath the Jews to their heirs upon death. In the 12th century, after anti-Jewish riots, the contemporaries commented that their population had 'greatly declined.'

As to how to solve the problem, the only way would be for Israel to defeat the Arabs overwhelmingly, and then dictate the terms for peace. Otherwise, the Arabs will never stop trying to destroy Israel.


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Two Trains... (Math)?

Boston and New York are approximately 280 miles apart. One Train leaves Boston traveling towards New York at an average speed of 80mph. Another train leaves New York at the same time traveling toward Boston at an average speed of 60 mph. (a) How long will it take them to meet? (b) How far has each train traveled when they meet?

I tried using d= rt but that didn't make much sense since I did
t = d/r which 280/80 = 3.5hours and 280/60 = 4.6 hours but the textbook says two. I'm a so confused. I need help with explanations!!

URGENT: Higher leaving cert maths questions?

1) The planets orbit is circular so when the comet crosses it's orbit it must be at the radius of the planet, 450 million km. This is not the case with the ellipse of the satellite.

So we have simultaneous equations x-2y = 4 and 3x^2+10y^2=150

x=(4-2y) => 3(4-2y)^2+10y^2=150 => expand and solve the quadratic, the answer is y=(12±√705)/11.
Since x is increasing, the lower value for x is crossed first so y=(12-√705)/11. Plug into x=4+2y to get x=4+2(12-√705)/11.

Now the distance to the origin in r^2=x^2+y^2 => r = √[((12-√705)/11)²+(4+2(12-√705)/11)²] = 1.89.

Since the radius of the planet was given as √25 = 5 in the equation but was at a distance of 450 million km we can assume 1 unit = 450,000,000/5 = 90,000,000 km so 1.89 => 170 million km

That was a horrific question!

2) simultaneous equations:
f=85t
g=100-65t

i) f = g when 85t = 100 - 65t => 100 = 150t => 2/3 hour = t = 40 mins

ii) at t=2/3, f = 85(2/3) = 56.7 km, 100-g = 65(2/3) = 43.3 km

that was easier

3) expand (x+a)^3 = a^3+3a^2x+3ax^2+x^3
so (x+a)^3+bx+cx= x^3-8 = a^3+3a^2x+3ax^2+x^3+bx+cx= x^3-8
=> a^3+3a^2x+3ax^2+bx+cx+8 = 0
3ax^2 + (3a+b+c)x + (8+a^3) = 0

Now, I think you made a mistake when you wrote this up because I could have any combination of b and c, I think you meant: (x+a)^3+bx+c=x^3-8 (not cx) which would mean we actually have:
3ax^2 + (3a+b)x + (8+a^3+c) = 0

The only way such that it always equals zero is to have all the coefficients as 0, so 3a=0, 3a+b=0 and 8+a^3+c=0.
So, a=0 so b=0 and c=-8 so the final equation is x^3-8=x^3-8...