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David covers a total of 240 miles journey, of which 120 miles are cove

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David covers a total of 240 miles journey, of which 120 miles are cove  [#permalink]

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New post Updated on: 28 Feb 2015, 00:47
1
4
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

76% (02:44) correct 24% (03:14) wrong based on 99 sessions

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David covers a total of 240 miles journey, of which 120 miles are covered at a constant speed and remaining 120 miles are covered at 10 mph more than first haf speed. Time take to cover second half of 240 miles is 1 hour less than first half of 240 miles. At what speed did David cover his second half of the journey?

(A) 30 mph
(B) 35 mph
(C) 40 mph
(D) 45 mph
(E) 50 mph

Originally posted by takeTWO on 28 Feb 2015, 00:42.
Last edited by Bunuel on 28 Feb 2015, 00:47, edited 1 time in total.
RENAMED THE TOPIC.
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Re: David covers a total of 240 miles journey, of which 120 miles are cove  [#permalink]

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New post 28 Feb 2015, 02:24
1
To be honest I had a lot of trouble with this one:

My only chance was to choose values and check whether they fit..

I tried 120/x = y and 120 / x-1 = 120/x + 10 but could not solve them

so..

120 / 4h = y , y = 30

120 / 3h = y + 10, y = 40

this is the only combination where this works, hence answer C, but is it the only approach to come to the solution?
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Re: David covers a total of 240 miles journey, of which 120 miles are cove  [#permalink]

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New post 28 Feb 2015, 07:26
LaxAvenger wrote:
To be honest I had a lot of trouble with this one:

My only chance was to choose values and check whether they fit..

I tried 120/x = y and 120 / x-1 = 120/x + 10 but could not solve them

so..

120 / 4h = y , y = 30

120 / 3h = y + 10, y = 40

this is the only combination where this works, hence answer C, but is it the only approach to come to the solution?


hi lax..
its quite easy through equations..
let the speed for first 120 =x, so for next =x+ 10..
as time saved is one hr in second case...
120/x=1+120/(x+10) ...
120x+1200=\(x^2\)+10x+120x...
\(x^2\)+10x-1200=0...
(x+40)(x-30)=0....so x=30....
speed in 2nd half=40...
ans C...
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Re: David covers a total of 240 miles journey, of which 120 miles are cove  [#permalink]

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New post 28 Feb 2015, 18:18
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Hi LaxAvenger,

This type of multi-part rate question is something that you'll likely see at least once on Test Day. The difficulty level will vary depending on when it shows up and how well you're performing.

Since the language "hints" that we'll need the Distance Formula (references to distance, speed and time), we can start there....

Distance = (Rate)(Time)

The first part of the prompt tell us nothing special about the Rate and the Time, but DOES tell us that the distance is HALF of 240 miles.

120 mi. = (R)(T)

The second part of the prompt tells us the Rate increases by 10mph and the Time decreases by 1 hour for the second half of the trip....

120 mi. = (R+10)(T-1)

We're asked for the SPEED during the SECOND HALF of the trip.

At this point, we have 2 variables and 2 unique equations, so you COULD do "system math" and solve the problem that way. You COULD also TEST THE ANSWERS (as you did). Here though, we're given a subtle "pattern matching" shortcut. It's interesting that ALL of the numbers involved are ROUND NUMBERS (even the answer choices are all round numbers). When a question is based on lots of multiplication and division, IF all of the numbers involved are "nice" INTEGERS, then there's most certainly some type of relationship among the numbers.

I'm going to focus on the 2 Rates. They differ by 10 AND they both divide (probably EVENLY) into 120. I'd be thinking about 10 and 20, 20 and 30, 30 and 40. NEXT, we know that the difference in Times is just 1 hour....

10mph and 20mph would be a difference of 6 hours
20mph and 30mph would be a difference of 2 hours
30mph and 40mph would be a difference of 1 hour. THAT's exactly what we're looking for. No complex math required.

Final Answer:

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Re: David covers a total of 240 miles journey, of which 120 miles are cove  [#permalink]

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New post 01 Mar 2015, 04:07
chetan2u wrote:
LaxAvenger wrote:
To be honest I had a lot of trouble with this one:

My only chance was to choose values and check whether they fit..

I tried 120/x = y and 120 / x-1 = 120/x + 10 but could not solve them

so..

120 / 4h = y , y = 30

120 / 3h = y + 10, y = 40

this is the only combination where this works, hence answer C, but is it the only approach to come to the solution?


hi lax..
its quite easy through equations..
let the speed for first 120 =x, so for next =x+ 10..
as time saved is one hr in second case...
120/x=1+120/(x+10) ...
120x+1200=\(x^2\)+10x+120x...
\(x^2\)+10x-1200=0...
(x+40)(x-30)=0....so x=30....
speed in 2nd half=40...
ans C...


Thanks for the explanation! My approach was that you cannot equal both equations

120/x = y
because time and speed of second trip is different
why can you equate them?
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Re: David covers a total of 240 miles journey, of which 120 miles are cove  [#permalink]

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New post 01 Mar 2015, 13:32
HI ALL,

I mentioned in my prior post how once you had the given equations....

120 = (R)(T)
120 = (R+10)(T-1)

....you could use "system math" to solve for the RATE on the SECOND DAY. Here's how that math "works":

Since we're after the value of R, we want to 'eliminate' the T.... We can rewrite the first equation as...

120/R = T

...Then substitute that value into the second equation....

120 = (R+10)[(120/R) - 1]

Now we can FOIL the equation...

120 = 120 - R + (1200/R) - 10
10 = -R + (1200/R)

Multiply everything by R....

10R = -(R^2) + 1200

And move everything to the "left side"....

R^2 +10R - 1200 = 0
(R + 40)(R - 30)

R = -40 or + 30

Since we can't have a negative speed and we want the speed during the SECOND HALF of the trip, the answer is 30 + 10 = 40.

Final Answer:

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Rich
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Re: David covers a total of 240 miles journey, of which 120 miles are cove  [#permalink]

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New post 05 Jun 2015, 06:59
Backsolving is best, moreover when we start test from C, as conventional, we find it is correct

Algebraically:

x-rate, t-time

xt=(x+10)*(t-1) => x=10t-10

120/t=10t-10, quadratic equation gives us t=4 or -3, so t=4. Easily get that x+10=40

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Re: David covers a total of 240 miles journey, of which 120 miles are cove  [#permalink]

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Re: David covers a total of 240 miles journey, of which 120 miles are cove   [#permalink] 27 Jun 2019, 23:56

David covers a total of 240 miles journey, of which 120 miles are cove

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