Numerical reasoning question

[Shicky]

Does anybody have a relatively quick method of solving this question? I cant imagine trial and error in the real test situation is a good idea

A printer prints 3500 characters a second and another prints 5200 characters a second. If the slower one starts at 9.15am and the second 15 minutes later, at what time will they have printed equal numbers of characters?

 

[SpaghettiOs]

It is fairly easily solvable using basic algebra.

Let the time in seconds after 9.30 am be 't'.

At 9:30 am, the second printer starts. By this time, the first printer has printed 900 seconds worth of characters.

The equation for when they are equal in characters is therefore:

3500(t+900)=5200t :: ie. 3500 times the time in seconds from 9:30 plus the extra characters, is equal to the time in seconds from 9:30 times 5200.

Then solve:

3500t + 3150000 = 5200t
3150000 = 1700t
t = 31500/17

900+31500/17=1905.88 which roughly equals 31.7 minutes after they start.

 

[Redman]

Or look at it logically:

3500 x 60 x 15 is total chtrs printed in the first 15 mins = 3150000
After this the difference in the two is 5200-3500=1700

So you have an excess print of 1700 chtrs to catch up with 3150000 already done.

3150000/1700 = 1852.94 s

1852.94/60= 30.88 m + 15m for the time the first one ran for.

Interesting I'm different to the algebra above, I'm probably wrong but I was bored and that's how I'd do it, hehe

 

[SpaghettiOs]

My bad. My algebra was completely wrong.

Original equation should have read:

3500t=5200(t-900)

Which gives the answer of 45.88 minutes. It's been a while since A-levels.

 

[Gaverick]

Or look at it logically:

3500 x 60 x 15 is total chtrs printed in the first 15 mins = 3150000
After this the difference in the two is 5200-3500=1700

So you have an excess print of 1700 chtrs to catch up with 3150000 already done.

3150000/1700 = 1852.94 s

1852.94/60= 30.88 m + 15m for the time the first one ran for.

Interesting I'm different to the algebra above, I'm probably wrong but I was bored and that's how I'd do it, hehe

That's how I did it too, came up with roughly 10am for an equal number of characters printed.

 

[Dave M]

They try to confuse you by using different units (minutes and seconds in this case). As soon as you look at it as 900 seconds the steps should become obvious.

 

[Cold_And_Miserable]

Does anybody have a relatively quick method of solving this question? I cant imagine trial and error in the real test situation is a good idea

A printer prints 3500 characters a second and another prints 5200 characters a second. If the slower one starts at 9.15am and the second 15 minutes later, at what time will they have printed equal numbers of characters?

Time taken for 5200t-3500t == 3500x15
t= 525/17

 

[GreatAuk]

Does anybody have a relatively quick method of solving this question? I cant imagine trial and error in the real test situation is a good idea

A printer prints 3500 characters a second and another prints 5200 characters a second. If the slower one starts at 9.15am and the second 15 minutes later, at what time will they have printed equal numbers of characters?

3500t + 3500*60*15 = 5200t

3500*60*15 = (5200-3500)t

(3500*60*15)/(5200-3500) = t

1852.9.. = t

1852.9/60 = 30.88

so 9:30 plus 30.88 minutes is 10:00 plus 0.88 of a minute:

10:01 is what I get.


I suppose my method would vary depending on whether I had a calculator (I'd approximate if I didn't), and if I had paper (I'd try and look at it in terms of the difference to make up and the difference in printing speed if I didn't get paper).