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Intern  Joined: 26 Feb 2011
Posts: 31
The time it took car A to travel 400 miles was 2 hours less than the  [#permalink]

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13 00:00

Difficulty:   45% (medium)

Question Stats: 72% (02:40) correct 28% (03:10) wrong based on 224 sessions

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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
Retired Moderator Joined: 20 Dec 2010
Posts: 1778
Re: The time it took car A to travel 400 miles was 2 hours less than the  [#permalink]

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Let B's average speed be b

$$\frac{400}{b+10} = \frac{400}{b}-2$$

$$\frac{400}{b+10} = \frac{400}{b}-2$$

$$(b+50)(b-40)=0$$

b=40 miles/h

Ans: "C"
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Math Expert V
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Posts: 55188
Re: The time it took car A to travel 400 miles was 2 hours less than the  [#permalink]

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Madelaine88 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 $$\frac{400}{40}=10=\frac{400}{40+10}+2=8+2$$

Answer: C.
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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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Madelaine88 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

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!

Answer is C

Cheers!
J Intern  Joined: 05 Dec 2013
Posts: 14
The time it took car A to travel 400 miles was 2 hours less  [#permalink]

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Bunuel wrote:
Madelaine88 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 $$\frac{400}{40}=10=\frac{400}{40+10}+2=8+2$$

Answer: C.

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!
Math Expert V
Joined: 02 Sep 2009
Posts: 55188
The time it took car A to travel 400 miles was 2 hours less  [#permalink]

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bparrish89 wrote:
Bunuel wrote:
Madelaine88 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 $$\frac{400}{40}=10=\frac{400}{40+10}+2=8+2$$

Answer: C.

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]

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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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1
.......................... 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

Answer = C
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Kindly press "+1 Kudos" to appreciate Intern  Joined: 14 Jun 2014
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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 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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Joined: 10 Apr 2018
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Location: United States (NC)
Re: The time it took car A to travel 400 miles was 2 hours less than the  [#permalink]

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Bunuel wrote:
Madelaine88 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 $$\frac{400}{40}=10=\frac{400}{40+10}+2=8+2$$

Answer: C.

Hi Bunuel,
This question needs an edit.
Should it read
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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Probus

~You Just Can't beat the person who never gives up~ Babe Ruth
Math Expert V
Joined: 02 Sep 2009
Posts: 55188
Re: The time it took car A to travel 400 miles was 2 hours less than the  [#permalink]

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Probus wrote:
Bunuel wrote:
Madelaine88 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 $$\frac{400}{40}=10=\frac{400}{40+10}+2=8+2$$

Answer: C.

Hi Bunuel,
This question needs an edit.
Should it read
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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The time it took car A to travel 400 miles was 2 hours less than the  [#permalink]

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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.

Final Answer:

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Rich
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www.empowergmat.com/ Re: The time it took car A to travel 400 miles was 2 hours less than the   [#permalink] 11 Apr 2019, 11:12
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