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Time and Distance Q

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Time and Distance Q

by Chinn_asama » Mon Sep 10, 2012 12:47 am
Hi

Can anyone explain this problem?

The distance between two stations A and B is 450 km. A train starts at 4 PM from A and moves towards B at an average speed of 60km/hr. Another train starts from B at 3.20 PM and move towards A at an avg.speed of 80km/hr. How far from A will the two trains meet and at what time?

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by neelgandham » Mon Sep 10, 2012 1:28 am
Step 1 : Distance travelled by second train travelling from B to A from 3:20 PM to 4 PM = Speed * time = 80*2/3(40 minutes) = 160/3 Kms

Step 2: At 4:00PM, distance between the trains = 450 - (160/3) kms

Step 3: Now, when the trains meet they will have travelled for the same time. If T1(and S1 the distance travelled) is the time taken by the train to travel from A to the meeting point and T2(and S2 the distance travelled) is the time taken by the other train.

T1 = S1/60
T2 = S2/80

T1 = T2; S1/60 = S2/80;
4S1 = 3S2.

But S1 + S2 = 450 - (160/3).
S1 + (4/3) S1 = 450 - (160/3).
(7/3)S1 = 1190/3
S1 = 170 kms.

p.s: You can also use a formula but I will leave that for you to find out.
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by Javoni » Mon Sep 10, 2012 2:40 am
So here's a one relevant shortcut: If two objects mowing towards each other add their respective speeds/rates. Here we go: Let x be the time when two trains meet. So for x hours train mowing from A will drive 60X km and the train moving from B will drive 80(X+2/3), 2/3 is 40 minutes, since B left earlier at 3:20, yep? Consequently, using the shortcut set forth above we get:
60X+80*(X+2/3) = 450, solving this easy equation we get that X = 119/42, that would be app 2.28 hours.

60X km, is the point, where the two trains met, yes? So we have 60*X = 60*119/42 = 170 km

So, I guess the answers to the questions would be : 1. 170 km and 2. 119/42 = 2.8(3) hrs

Please, don't hesitate to correct me if I went awry buddy!

Chinn_asama wrote:Hi

Can anyone explain this problem?

The distance between two stations A and B is 450 km. A train starts at 4 PM from A and moves towards B at an average speed of 60km/hr. Another train starts from B at 3.20 PM and move towards A at an avg.speed of 80km/hr. How far from A will the two trains meet and at what time?

THANX
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    by Chinn_asama » Mon Sep 10, 2012 4:46 am
    Could you please explain why 40 min is taken as time?
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    by Brent@GMATPrepNow » Mon Sep 10, 2012 6:34 am
    Chinn_asama wrote: The distance between two stations A and B is 450 km. A train starts at 4 PM from A and moves towards B at an average speed of 60km/hr. Another train starts from B at 3.20 PM and move towards A at an avg.speed of 80km/hr. How far from A will the two trains meet and at what time?
    I like to begin with a word equation. Here, I'll call the train leaving from station A the "A-train" and the other will be called the "B-train."

    Since the total distance is 450 km, we can write:
    (Distance the A-train travels) + (Distance the B-train travels) = 450

    Note: We'll start the clock at 4pm. So, at 4pm, the B-train has already been traveling for 40 minutes (i.e., 2/3 of an hour). So, at 4pm, the B-train has already traveled a distance of (2/3)(80) km. In other words, the B-train has already traveled 160/3 km

    Let's let t = the amount of time that has elapsed since 4pm.

    We'll write: (60t) + (80t + 160/3) = 450
    To solve, we'll simplify: 140t + 160/3 = 450
    Multiply both sides by 3: 420t + 160 = 1350
    Subtract 160 from both sides: 420t = 1190
    Divide both sides by 420: t = 1190/420 = 119/42 hours

    So, 119/42 hours after 4pm, the two trains meet. How far from Station A are they at this point?

    Well, Train-A has been traveling at 60 kmh for 119/42 hours.
    So, the distance from Station A will be (60)(119/42) km
    (60)(119/42) = 170, So, the trains are 170 km from Station A.

    Cheers,
    Brent
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    by Chinn_asama » Mon Sep 10, 2012 10:06 am
    In the book I am referring, it is solved differently.

    Firt step. [Time taken by B to cover 450-x km]-[Time taken by A to cover x km] = 40/60

    and if you calculate it you get the answer. BUT I did not understand the first step, Can someone explain the first step?






    thanx
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