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

Question

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

Source: Chili Hot GMAT

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Official Answer

C

A) 20
B) 40
C) 60
D) 80
E) 100

Source: Chili Hot GMAT

KarishmaB · Accepted Answer

You can also do it by plugging in the options. The correct option will be the one which will divide 240 to give a certain time and which when increased by 20 will again divide 240 to give 1 hr less.
So say, if speed is 20, 240/20 = 12 hr but 240/40 = 6 hrs (this is a reduction of 6 hrs - clearly wrong. We need a reduction of only 1 hr)
Say, if speed is 60, 240/60 = 4 hrs and 240/80 = 3 hrs (a reduction of 1 hr -> Correct answer)

Answer (C)

Ankur9 · Answer

Time taken with the normal speed = D/S
Time taken when the speed is 20 miles per hour faster = D/(S+20)
since it takes 1 hour less if the submarine had traveled 20 miles per hour faster.
therefore D/S - D/(S+20) = 1
where D = 240 miles
solving it to get  S^2+20S-4800=0 
S= 60 , -80. 
since speed cannot be negative therefore S = 60 which is same as the average speed 
why???
time taken to cover 240 miles with speed 60 = 240/60--->4hours
Average speed = total distance travelled/ total time taken
=240/4 = 60
Thus C

vietnammba · Answer

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.

PareshGmat · Answer

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

AliciaSierra · Answer

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

akumar5 · Answer

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

Temurkhon · Answer

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

ScottTargetTestPrep · Answer

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

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