Two trains traveling toward each other on parallel tracks at constant

Question

Two trains traveling toward each other on parallel tracks at constant rates of 50 miles per hour and 60 miles per hour are 285 miles apart. How far apart will they be 2 hours before their engine meet?

(A) 110
(B) 120
(C) 150
(D) 200
(E) 220

KarishmaB · Accepted Answer

It's a relative speed question. When they travel toward each other, their relative speed is the sum of the two speeds (50 + 60 = 110 mph) In 2 hrs, they will together cover a distance of 2*110 = 220 miles. Hence, 2 hrs before their engines meet, distance between them will be 220 miles. Answer (E) Check this video for when to use relative speed: https://youtu.be/wrYxeZ2WsEM

Subhrajyoti · Answer

I am not sure how can we say the gap between two bodies is same as sum of the distance travelled by them.

Maybe I am missing something here.

Requesting you all to give your inputs

dollytaneja51 · Answer

Both trains together will take 285/(60+50) hours to meet
i.e. 2 hours 35 mins approx
We need to find how far apart trains will be 2 hours before their engine meet
Therefore, train 1 will be at (50/60*35) miles = 29 miles approx
And Train 2 will be (60/60*35) miles = 35 miles
285 - (29+35) = 221 miles
Answer E which is 220 miles.

I know my approach for solving is not correct.

Can you provide the solution?

Posted from my mobile device

Subhrajyoti · Answer

I am not sure i understand. How can sum of speeds define the gap between two moving objects. It tells me how much they have traveled.

The distance here is 285 miles, so the sum of the distance traveled - distance , shouldn't that be distance between them.

KarishmaB · Answer

There is some gap between them. They travel towards each other for 2 hrs to cover that gap and that is when they meet. Their speeds are fixed at 50 mph and 60 mph. 
So in 2 hrs, one of them travels 100 miles and the other travels 120 miles. Together they travel 220 miles in 2 hrs to meet. So the gap between them 2 hrs ago must have been 220 miles. 
Say if the gap between them were 330 miles, they would have taken 3 hrs to meet. They would not have met in 2 hrs. 2 hrs happened because the gap between them was 220 miles.

mbafinhopeful · Answer

Time it would take for the trains to meet =  \frac{285}{(50+60)} = 2.59  hours =  2  hours and  35  mins (approx.)

Distance between the trains two hours before they meet =  285  - Distance travelled by the trains in  35  mins =  285 - \frac{110*35}{60} = 285 - 65  (approx.) =  220  (approx.) Ans E.

Archit3110 · Answer

relative speed ; 110 miles
time ; 2 hrs 
distance ; 2*110 ; 220 miles
IMO E

SumedhaD1452 · Answer

Hello, could you please help me understand this further? The gap between them is 285 miles, their relative speed is 110 mph, which means they will meet at 285/110 hours = ~2.5 hours. How is it that "They travel towards each other for 2 hrs to cover that gap and that is when they meet"?

Bunuel · Answer

The initial distance between the trains does not matter. When they actually meet, that also does not matter. What matters is: what will the distance be between the trains two hours before they meet. Two hours before they meet, the distance is exactly what the trains will cover in these two hours. And in two hours, the trains together cover 2 * (50 + 60) = 220 miles.

Two trains traveling toward each other on parallel tracks at constant

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Two trains traveling toward each other on parallel tracks at constant

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