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# The time it took car A to travel 400 miles was 2 hours less than the

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The time it took car A to travel 400 miles was 2 hours less than the [#permalink]
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The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed in miles per hour?

A. 20
B. 30
C. 40
D. 50
E. 80

Agree with Bunuel, in these problems one will find it easier to plug in answer choices, that is, backsolving

One gets

400/B+10 - 400/B = 2

So beginning with C one gets that 10 - 8 = 2

So bingo!

Cheers!
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The time it took car A to travel 400 miles was 2 hours less [#permalink]
Bunuel wrote:
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed in miles per hour?

A. 20
B. 30
C. 40
D. 50
E. 80

Let the rate of B be $$x$$ miles per hour, then the rate of A would be $$x+10$$ miles per hour.

We also know that the time of B equals to time of A + 2: $$\frac{400}{x}=\frac{400}{x+10}+2$$, from this point it's better to plug the answer choices rather than to solve the quadratics. You can quickly find that $$\frac{400}{40}=10=\frac{400}{40+10}+2=8+2$$

I'm struggling with this one for some odd reason:

The setup for my work was as follows
Car B: Rate = R + 10, Time = T + 2, Distance = 400
Car A: Rate = R, Time = T, Distance = 400

I then substituted B's Rate (400/T) into Ys equation --> giving me --> (400 / T) + 10 = (400 / T - 2)
After solving this out, I got T = 20, therefore Car B's average speed is 20mph.

Can either of you help me out with where I went wrong here. Much appreciated. Just over a month from my first GMAT experience!
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The time it took car A to travel 400 miles was 2 hours less [#permalink]
bparrish89 wrote:
Bunuel wrote:
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed in miles per hour?

A. 20
B. 30
C. 40
D. 50
E. 80

Let the rate of B be $$x$$ miles per hour, then the rate of A would be $$x+10$$ miles per hour.

We also know that the time of B equals to time of A + 2: $$\frac{400}{x}=\frac{400}{x+10}+2$$, from this point it's better to plug the answer choices rather than to solve the quadratics. You can quickly find that $$\frac{400}{40}=10=\frac{400}{40+10}+2=8+2$$

I'm struggling with this one for some odd reason:

The setup for my work was as follows
Car B: Rate = R + 10, Time = T + 2, Distance = 400
Car A: Rate = R, Time = T, Distance = 400

I then substituted B's Rate (400/T) into Ys equation --> giving me --> (400 / T) + 10 = (400 / T - 2)
After solving this out, I got T = 20, therefore Car B's average speed is 20mph.

Can either of you help me out with where I went wrong here. Much appreciated. Just over a month from my first GMAT experience!

We are given that Car As average speed was 10 miles per hour greater than that of car B, thus if you say that the rate of A is R miles per hour, then the rate of B is R-10 miles per hour (not R+10).

The equation should be 400/T -10 = 400/(T+2) --> T=8 --> B's rate = 400/(T+2) = 40.

Hope it's clear.
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Re: The time it took car A to travel 400 miles was 2 hours less than the [#permalink]
To be academic with use GMAT strategy)

R * T = D
A x-2= 400
B x = 400

Question is what is the rate of B. I agree that backsolving is the best strategy and start with C. If R of B=40 then x=10 and R of A=50 and this is 10 more than B. So answer is C
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Re: The time it took car A to travel 400 miles was 2 hours less than the [#permalink]
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.......................... A................. B

Time .................. t .................. t+2

Speed ............... s+10 ............... s

t(s+10) = s(t+2) = 400

s = 5t

Substitute value of t in any of the formed equation:

$$\frac{s}{5} (s+10) = 400$$

$$s^2 + 10s - 2000 = 0$$

Speed of B (s) = 40

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Re: The time it took car A to travel 400 miles was 2 hours less than the [#permalink]
The first step should be mentioned here: Translate the task into numbers and variables !

Here you have a lot of different possibilities just 2 examples:

I. (r+10) * (t-2) =400
II. r * t = 400

OR:

I. (r+10) * t = 400
II. r * (t+2) = 400

As you can see, no we have 2 equations with 2 variables... tons of different possibilities to solve this as well:
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Re: The time it took car A to travel 400 miles was 2 hours less than the [#permalink]
Bunuel wrote:
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car As average speed was 10 miles per hour greater than that of car B, what was car Bs average speed in miles per hour?
A/ 20
B/ 30
C/ 40
D/ 50
E/ 80

Let the rate of B be $$x$$ miles per hour, then the rate of A would be $$x+10$$ miles per hour.

We also know that the time of B equals to time of A + 2: $$\frac{400}{x}=\frac{400}{x+10}+2$$, from this point it's better to plug the answer choices rather than to solve the quadratics. You can quickly find that $$\frac{400}{40}=10=\frac{400}{40+10}+2=8+2$$

Hi Bunuel,
This question needs an edit.
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A ‘s average speed was 10 mi greater than that of average speed of Car B , the what was Car B’s average speed in miles per hour?

Probus
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Re: The time it took car A to travel 400 miles was 2 hours less than the [#permalink]
Probus wrote:
Bunuel wrote:
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car As average speed was 10 miles per hour greater than that of car B, what was car B`s average speed in miles per hour?
A/ 20
B/ 30
C/ 40
D/ 50
E/ 80

Let the rate of B be $$x$$ miles per hour, then the rate of A would be $$x+10$$ miles per hour.

We also know that the time of B equals to time of A + 2: $$\frac{400}{x}=\frac{400}{x+10}+2$$, from this point it's better to plug the answer choices rather than to solve the quadratics. You can quickly find that $$\frac{400}{40}=10=\frac{400}{40+10}+2=8+2$$

Hi Bunuel,
This question needs an edit.
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A ‘s average speed was 10 mi greater than that of average speed of Car B , the what was Car B’s average speed in miles per hour?

Probus

_______________
Edited. Thank you.
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Re: The time it took car A to travel 400 miles was 2 hours less than the [#permalink]
Hi swerve,

We're told that the time it took car A to travel 400 miles was 2 hours LESS than the time it took car B to travel the same distance and car A's average speed was 10 miles per hour GREATER than that of car B. We're asked for car B's average speed in miles per hour. This question can be approached in a couple of different ways. Since it's essentially about basic arithmetic (re: two 'pairs' of numbers that have a product of 400), you would likely find it fastest to TEST THE ANSWERS.

To start, the difference in the time that the two cars traveled is exactly 2 hours and we know that Car B was going exactly 10 mph slower than Car A. Based on the prompt and the answer choices, we're clearly dealing with nice 'round' numbers, so let's start with an answer that divides evenly into 400...

Let's TEST Answer C: 40 miles/hour

IF.... Car B is traveling 40 mph, then it takes 400/40 = 10 hours to complete that drive.
We're told that Car A's speed is 10 mph greater than Car B's speed, so....
Car A is traveling 50 mph... and that would take 400/50 = 8 hours to complete that drive.
Here, the difference in travel time is exactly 2 hours - and this matches what we were told - so this MUST be the answer.

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Re: The time it took car A to travel 400 miles was 2 hours less than the [#permalink]
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The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed in miles per hour?

A. 20
B. 30
C. 40
D. 50
E. 80

Car A's average speed was 10 miles per hour greater than that of car B
Let x = Car B's average speed
So, x + 10 = Car A's average speed

The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance
In other words: (car A's travel time) = (car B's travel time) - 2

time = distance/speed
So, we get: 400/(x + 10)) = 400/x - 2

NOTE: At this point, we can either test the five answer choices to see which one satisfies the above equation, or we can solve the equation algebraically.
Although testing the answer choices is probably faster, let's solve the equation algebraically
Multiply both sides of the equation by (x + 10) to get: 400 = 400(x + 10)/x - (x + 10)(2)
Multiply both sides of the equation by x to get: 400x = 400(x + 10) - (x)(x + 10)(2)
Expand: 400x = 400x + 4000 - 2x² - 20x
Subtract 400x from both sides to get: 0 = 4000 - 2x² - 20x
Multiply both sides by -1 to get: 0 = -4000 + 2x² + 20x
Rewrite as follows: 2x² + 20x - 4000 = 0
Divide both sides by 2 to get: x² + 10x - 2000 = 0
Factor: (x + 50)(x - 40) = 0
So, EITHER x = -50 OR x = 40
Since the speed can't be negative, it must be the case that x = 40

Cheers,
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Re: The time it took car A to travel 400 miles was 2 hours less than the [#permalink]
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[quote="Madelaine88"]The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed in miles per hour?

Instead of doing the long calculation it is better to put up the option, calculation is not difficult also.
Option C
B's speed =40 therefore A's speed =50
Time taken by B = 400/40=10
Time taken by A = 400/50 =8
It is two hours less therefore this is the answer.

Posted from my mobile device
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The time it took car A to travel 400 miles was 2 hours less than the [#permalink]
Remember GMAT will punish you if you a stricter of formulas and methods, more so if you don't look at the type of answers given.

If you've comprehended the question, you can get the answer in 30 seconds or less if you glance at the answers choices given.

Let's go!!!!

So car A is faster than car B by 2 hrs or 10kph in the 400 distance and we are being asked the speed of car B.

Since we have everything we need to used to calculate speed, we just need to find two speeds that have a 2hr and 10kph difference.

so take the distance/ speed = 400 / Answer A = 400 / 20 = 20.

if I plus 10 = 400 / 30.

You keep testing the answers and you can quickly realize that 400 / 40 = 10hrs and 400 / 50 = 8 hrs

and so this are our two speeds that differ by 10kph and 2hrs difference when covering the 400km distance.

Since car B is the slower one, then it's the one traveling at 40kph.