✡Justin – ג ‘סטין✡: Help on homework! math!?
I would like for someone to explain for me to do a problem like this or give me the formula! please!
Train A is goin 200 m/ph from point A and Train B is Goin 50 m/ph from point B the distance between them is 1,000 miles. please help1
when will they meet
Answers and Views:
Answer by Melissa
What’s the question?
Since you have not given the necessary details I am assuming that both the trains are of negligible lengths ( As compared to the length of the path ), and are running on two parallel tracks. As such there may be two cases ( of course we cant rule out many other cases eg : the tracks may be inclined to each other at some angle ).
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Case 1 Both the trains are running towards each other.
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If they meet after “t” hrs at a distance of “d” miles from A, then, time taken by A to cover “d” miles by Train A = time taken by Train B to cover ( 1000 – d ) miles.
=> ( d/200 ) = t = [ (1000 – d ) / 50 ] hrs ………………… (i)
=> ( d/200 ) = (1000 – d ) / 50
=> 50 ( d/200 ) = (1000 – d )
=> d/4 = (1000 – d )
=> d = 4 (1000 – d )
=> d = 4000 – 4d
=> 5d = 4000
=> d = 800 miles => t = 800/200 hrs. = 4 hrs ……. Answer Answer
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Case 2 Trains A and B are running in the same direction and A is chasing B.
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Again let Train A be meeting B after travelling for “t” hrs.at a distance “d” miles from B.
=> (1000 + d) / 200 = t = d/50 …………….. (ii)
=> (1000 + d) = 200 ( d/50 )
=> 1000 + d = 4 d
=> d = 1000/3 miles.
=> t = d / 50 = 1000 / ( 50×3 ) = 20/3 hrs = 6 hrs 20 mins …………… Answer Answer.
Dr. P.K.Tandon
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Answer by Marley Klet t = hours traveled before they meet
200t + 50t = 1000
250t = 1000
t = 4
they will met 4 hours from the time they start.
that’s it! 😉
Answer by MathBioMajorIf Train A is traveling at 200 mph, then the distance it will have traveled when it meets Train B is given by this equation:
d = 200t.
The distance Train B will have traveled when the two trains meet is given by this equation:
d’ = 50t.
Assuming the trains leave at the same time, when they meet the sum of the distances they will have covered will be equal to their separation distance at their time of departure:
d + d’ = 1,000.
Now all we have to do is plug in the expressions for d and d’, and solve for t:
200t + 50t = 1,000
250t = 1,000
t = 1,000/250
t = 4.
The two trains will meet after 4 hours.
Here is another scenario which is frequently encountered in this type of problem. Suppose that the trains leave at different times. Then the time differential must be accounted for in the formula for the total distance traveled when the trains meet. So suppose Train B leaves 4 hours earlier than Train A. Then when the trains meet, its distance traveled will be given by the equation d’ = 50(t + 4) because it will have been traveling 4 more hours than Train A. So this would be the result:
d + d’ = 1,000
200t + 50(t + 4) = 1,000
200t + 50t + 200 = 1,000
250t = 1,000 – 200
250t = 800
t = 800/250
t = 8/2.5
t = 3.2 hours, or 3 hours and 12 minutes.
What this means is that Train B will only have to continue traveling 3.2 hours more until it meets Train A. So, Train A will have to travel only 3.2 hours, and Train B will have to travel (t + 4) = (3.2 + 4) = 7.2 hours.
We can also look at this same scenario from a different perspective. If Train B has been traveling t hours, which is 4 more hours than Train A, then Train A has been traveling t’ = (t – 4) hours with respect to Train A. So we can plug t’ = (t – 4) into the previous formula to get this:
d + d’ = 1,000
200(t – 4) + 50t = 1,000
200t – 800 + 50t = 1,000
250t = 1,000 + 800
250t = 1,800
t = 1,800/250
t = 7.2 hours.
Note that 7.2 hours is actually the total amount of time which Train B must travel until the trains meet. But, Train A only travels (t – 4) = (7.2 – 4) = 3.2 hours, which agrees with the previous answer.
It is easy to see that these sorts of problems require quite a bit of flexibility of thinking, and the ability to define and modify the necessary equations as needed. This is a skill that you will acquire as you progress through your study of mathematics.
Answer by acadia101Distance between A & B is 1000 miles.
Speed of train A = 200 miles/hr
Speed of train B = 50 miles/hr
Speed of train A & train B (together)= 250 miles/hr.
Time ( when they will meet) = distance/ speed
= 1000 / 250
= 4 hrs.
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