two problems need help

[skawal]

1. if two trains 120 miles apart and travelling toward each other at a constant rate of 30mph and 40mph, respectively,how far apart will they be 1 hour before meet? ans: A)10 B)30 C)40 D)50 E)70

2. COL A COL B
100,210*90,021 100,021*90210

for question 2 show me a shortcut.

[gunzi]

You can begin by splitting the numbers:
(100,000+210)*(90,000+21) (100,000+21)*(90,000+210)
By additive multiplication, its clear that 100,000*90,000 and 21*210 can be eliminated from both sides.
We’re left with –
A B
210*90,000 21*90,000
+21*100,000 +210*100,000
Column B is greater!!!
I’m sure there’s a still quicker solution…I’d like to know too.

[mickgreen58]

1. if two trains 120 miles apart and travelling toward each other at a constant rate of 30mph and 40mph, respectively,how far apart will they be 1 hour before meet? ans: A)10 B)30 C)40 D)50 E)70

1) Find the time it will take for them to meet:
120 = 30t + 40t = 12/7

12/7 is not easy to work with when plug back in, so I used the decimal form:
12/7 = 1.714 and just rounded to 1.71.

2) Now, subtract 1 from the total time, 1.71 - 1 = .71.

.71 is extremely close to .70 and 7/10 is easier to work with than .71.

3) Plug back into your equation:
120 = 30(7/10) + 40(7/10)
120 = 21 + 28
120 - 49 = 71

[gunzi]

My answer to the first question is E)70 miles.
Let the trains approaching from opposite directions meet at any point X. 1 hour ago, they would have been 30 miles and 40 miles away from X (in opposite directions) respectively. total distance between them = 70 miles.
easier to make a rough sketch and intuitively work out the answer. Any flaw with my argument??

[skawal]

dear
gungi

your shortcut reply cannot be understood. please do clear.

[gunzi]

lol @ gungi..
Skawal, which question do you wnat me to explain - 1 or 2?

[skawal]

ooooooooooopppps.no.2

[skawal]

sorry no.1. not no.2

[gunzi]

Two trains are 120 miles apart.Suppose they meet at any point X in that 120 mile distance. (draw a line for convenience and mark X somewhere towards the middle)
Train A moves at 30mph and Train B at 40mph.
One hour back Train A would have been 30miles away from X (because it covers a distance of 30 miles in 1 hour) and Train B would have been 40 miles away from X in the opposite direction. (you can try making a line segment – mark X on it and then points A and B to get a clearer picture)
The distance between A and B = 30+40 = 70 MILES!
This is quite simple intuitively… draw a line and try to visual it..thats why I avoided the calculation.
Hope this helps…

[skawal]

dear
gungi,

at last i able to visualize it.gre question should be like this.however that was a powerprep question