Two Trains... (Math)?

Question

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!!

Answer 1

Use the combined speed 80 + 60 = 140
280/140 = 2 hours
Then the train traveling at 80 miles an hour for 2 hours travels 160 miles.
And the train traveling at 60 miles an hour for 2 hours travels 120 miles.

Answer 2

Your error is that by taking 280 miles as the distance, you assume that both train traveled the whole distance, which is not the case when the meet somewhere between the two cities.

Since they both left at the same time, what is equal is the time.
So you have D1/80 = t and D2/60 =t, or

D1/80 = D2/60

You also have that D1 + D2 = 280

The first equation gives:
D1 = 80 * D2 / 60 or 4/3 D2

So, we can replace the value of D1 in the second equation:

4/3 D2 + D2 = 280
7/3 D2 = 280
1/3 D2 = 40
D2 = 120 miles

And since D1 + D2 is 280, D1 is 160 miles.

At 80 miles per hour, to cross 160 miles requires 2 hours.

Answer 3

When 2 trains meets, this means they have covered combine miles of 280.

T= Time

Train 1 =80T
Train 2 = 60T

80T+60T=280

Thus T= 2 (Algebra)

Train 1 = 80(2) = 160 miles
Train 2 = 60(2) = 120 miles

Answer 4

This Site Might Help You.

RE:
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...

Answer 5

When the two trains meet, they have both been travelling for the same time, say x hours, and the combined distance that they have travelled is 280 miles. one train has travelled 60x miles, and the other 80x miles, so

60x + 80x = 280

140x = 280

x = 2 hours. Hope this helps, Twiggy.

Answer 6

Total distance from Boston to New york is 280miles.
speed of first train T1=80mph.
speed of second train T2=60mph

duration of train 1 to complete the journey= distance/speed of train 1
i.e duration of T1 =(280/80)............ which is 7/2 hrs.
duration of train 2 to complete the journey= distance/speed of train 2
i.e duration of T2 =(280/60)............ which is 14/3 hrs.

to find meeting time:-
first we need to find relative speed of two trains.

Relative speed = speed of T1 + speed of T2

Relative speed = 60+80 => 140mph

time taken for two trains to meet each other = distance / relative speed

=> 280/140
= 2 hrs.. (from the time of start)

note: relative speed = speed 1 + speed 2 (In case of opposite direction)
relative speed = speed 1 - speed 2 (In case of same direction)