On a reconnaissance mission, a state-of-the-art nuclear powered submar

Is the correct answer C ( 60)?
If average speed is x, time for actual journey is t => x = 240/t
If the speed is 20m more, time travel is 1h less => x+20 =240/t-1

=> 240/t + 20 = 240/t-1
=> 20t2 - 20t - 240 =0 => t=4 => x = 240/4 = 60.

Answer = C = 60

Speed ........................ Time ........................ Distance

x ................................. \(\frac{240}{x}\) ............................ 240 (Assume x = actual speed)

x+20 ......................... \(\frac{240}{x} - 1\) ........................... 240 (Speed increases by 20, travel time decreases by 1 Hr)

Setting up the equation

\((x+20)(\frac{240}{x}-1) = 240\)

\(240 - x + \frac{4800}{x} - 20 = 240\)

\(x^2 + 20x - 4800 = 0\)

x = 60

Speed = Distance/Time
Time= Distance/Speed

Time taken with the normal speed = D/S
Time taken when speed is 20 miles/hr faster = D/(S+20)

as per question, submarine takes one hour less when traveled with S+20 speed.
Therefore, D/S-D/(S+20) = 1

Solve above equation for S, where D= 240

we will get S= 60 & -80. Speed can never be in negative integer.

So Average Speed is 60.

Answer: C

Lets x be the rate of the sub.

Time taken to cover 240 miles =240/x

Now, when the rate is increased by 20 miles ,time taken to cover the same distance=240/(x+20)

Given that the difference between both the time is 1 hr.

So 240/x -240/(x+20)=1
240x + 4800 -240x =x(x+20)
x^2 +20 -4800=0
x= -80,60

Since rate is a positive quantity its 60mph

Answer C

In using algebra, sometimes, we need to stop when necessary and use backsolving

240/x - 240/(x+20) =1, now we can backsolve

take C: 240/60 - 240/80=1. Correct

C

P.S. By continuing to solve the equation we get quadratic one that requires more time than backsolving

[quote=]

On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 240 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 1 hour less if the submarine had traveled 20 miles per hour faster. What was the average speed, in miles per hour, for the actual journey?

A) 20
B) 40
C) 60
D) 80
E) 100 [/quote]

We are given that a submarine traveled 240 miles to reposition itself in the proximity of an aircraft carrier. We are also given that had the submarine traveled 20 mph faster, the journey would have taken 1 hour less.

We can let the original rate = r and the theoretical rate = r + 20. Thus, the actual time was 240/r and the theoretical time was 240/(r + 20). We can create the following “time” equation to determine r.

240/(r + 20) + 1 = 240/r

We can multiply the entire equation by r(r + 20) and we have:

240r + r(r+20) = 240(r + 20)

240r + r^2 + 20r = 240r + 4800

r^2 + 20r - 4800 = 0

(r + 80)(r - 60) = 0

r = -80 or r = 60

Since r must be positive, r = 60.

Answer: C

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.