The time it took car P to travel 600 miles was 2 hours less than the

Question

The time it took car P to travel 600 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?

A. 40
B. 50
C. 60
D. 70
E. 80

A. 40
B. 50
C. 60
D. 70
E. 80

grv805 · Answer

Let speed of car R be=x
Then speed of car P= x+10
A/Q,
(600/x)-(600/(x+10))=2

Solving for x=50 miles\hr.

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CrackverbalGMAT · Answer

Time = \frac{Distance }{ Speed}

P travels faster than R, since it took 2 hours lesser.

Therefore Time of R - Time of P = 2 - - (1)

Let speed of R = x, then speed of P = x + 10

Distance = 600 miles

Putting in (1)

\frac{600}{x} - \frac{600 }{ x + 10} = 2

There are 2 ways to go about this.

(a) Substitute options for x. In this putting x = 50 gives us  \frac{600}{50} - \frac{600 }{ 60} = 12 - 10 = 2

(b) Form the quadratic equation and solve it

600(x + 10) - 600x = 2(x)(x+10)

6000 = 2(x^2 + 10x)

x^2 + 10x - 3000 = 0

Splitting the middle terms as +60 and -50, we get

x^2 + 60x - 50x - 3000 = 0

x (x + 60) - 50(x + 60) = 0

(x + 60) (x - 50) = 0

Therefore x = 50

Option B

Arun Kumar

MathRevolution · Answer

Rather than going for assuming speed to be 'x', try doing by hit n trial.

1st chance:   (Assume) Time taken by R = 12 hours

Distance: 600 miles.

Speed: 50 miles per hour.

Therfore, Time taken by P = 12 - 2 = 10 hours 
Distance: 600 miles.

Speed: 60 miles per hour.

Car P’s average speed was 10 miles per hour greater than that of car R - Proved.

2nd chance: Try with options.

Suppose we pick option D.
But try taking the option that divides 600 completely. So, try taking 60.

R = 60 miles per hour - Distance = 600 - Time taken = 10 hour.
P = 60+10 = 70 miles per hour - Distance = 600 - Time taken = 9.x hour (not 2 hours less than R).

Answer B

daniformic · Answer

I tried with options 
I usually start picking B out. I know that:

R: Avg: y Time: x Distance: 600
P: Avg: y+10 Time: x-2 Distance: 600
If i try with answer B, i get:
R: Avg: 50 Time: 12 Distance: 600
P: Avg: 60 Time: 10 Distance: 600
 YES!

Answer -> B

ashmitakhan · Answer

I always get confused with these types of problems. So here's another approach. It's a little lengthy but easy! Since, the numbers are very simple, the calculations should not take a lot of time!

Let's use the options: A: If Speed of R= 40 mph then time taken will be, t=d/s t= 600/40= 15 hours Now, we know, that P(t)= t-2= 13 And P(s)= s+10= 50 mph D= s*t and we know D=600 miles So, now, D= 13*50= 650 miles Not our answer B: R=50 mph t= 600/50= 12hours Now, P(t)= 10 hours S= 60 mph D= 60*10= 600 miles CORRECT Hence, Speed for R should be 50 mph Correct answer is B.

ScottTargetTestPrep · Answer

Solution:
 
Since the answer choices are easy numbers, let’s solve the problem numerically instead of algebraically. That is, we can check each answer choice until we find the correct answer.

If car R’s speed is 40 mph, then car P’s speed is 50 mph. Furthermore, it will take car R 600/40 = 15 hours and car P 600/50 = 12 hours to travel 600 miles. However, since 12 is not 2 less than 15, we see that choice A is not the correct answer.

If car R’s speed is 50 mph, then car P’s speed is 60 mph. Furthermore, it will take car R 600/50 = 12 hours and car P 600/60 = 10 hours to travel 600 miles. However, since 10 is 2 less than 12, we see that choice B is the correct answer.

Answer: B

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The time it took car P to travel 600 miles was 2 hours less than the

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