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

\(Time = \frac{Distance }{ Speed}\)

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

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

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.

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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