Alan drove from city A to city B at an average speed of

Question

Alan drove from city A to city B at an average speed of 50 miles per hour and returned back along the same route at an average speed of 60 miles per hour. If the total driving time of the journey was 11 hours, how many minutes did Alan take to drive from city B to city A?

A. 5

B. 6

C. 50

D. 300

E. 360

A. 5​

B. 6​

C. 50​

D. 300​

E. 360​

MARVEL13 · Answer

A to B average speed of 50 m/h
B to A average speed of 60 m/h

Total time - 11 hours

Time for B to A?

Total distance is 2D
Total Average speed will be (2*50*60) /(50+60) -->
600/11

Time taken from B to A will be

11= 2D*11/600

D = 300

Therefore time taken with speed of 60m/h and distance of 300 m will be 300/6 = 5 hrs

Or 300 minutes.

Posted from my mobile device

CrackverbalGMAT · Answer

One more method is by eliminating Options.

If the speed from A to B and B to A were the same, then it would have taken 11/2 = 5.5 hours = 330 minutes each way.

Since the speed from B to A (60 km/hr) is greater than that from A to B (50 km/hr), the time taken would be a little lesser than 330 minutes, and from the options,  Option D  = 300 minutes would be a logical conclusion.

Please Note that if the options were closer to 300 and elimination is not possible then the problem should be solved using the concept of average speeds.

Arun Kumar

Piyush1993 · Answer

50(11-x) = 60x
X= 5 hr or 300 mins

Posted from my mobile device

MathRevolution · Answer

Logic I:

The distance traveled is the same. Let the distance traveled is d miles.

Speed =  \frac{Distance }{ Time}

=> Time =  \frac{Distance }{ Speed}

=> 11 =  \frac{d }{ 50}  +  \frac{d }{ 60}

=> 11 =  \frac{6d+5d }{ 300 }

=> d = 300 miles.

Time =  \frac{Distance }{ Speed}  (From B to A)

=> Time =  \frac{300 }{ 60}  = 5 hours .

In minutes, 5 * 60 = 300 minutes.

Answer D

Logic II:

The distance traveled is the same. Therefore, Average speed =  \frac{2 * 50 * 60}{ 50 + 60 } .

=>  \frac{2 * 50 * 60 }{ 110}

=> Total Distance = Speed * Time

=> Total Distance =  \frac{2 * 50 * 60 }{ 110}  * 11 = 600

=> Distance from B to A: 300 miles.

=> Time =  \frac{300 }{ 60}  = 5 hours .

In minutes, 5 * 60 = 300 minutes.

Answer D

daniformic · Answer

More simply:
A to B and B to A -> 11h
A to B -> 50m/h
B to A -> 60m/h
50≅60
11h/2=5.3h
A:50*5.3h=265
B:60*5.3h=318
I need more time for A and less for B:
A:50*6h=300
B:60*5h=300
YES!

Answer -> D

ashmitakhan · Answer

I used logic instead of calculating. Let's eliminate answers:
A,B,C cannot be the answer logically speaking.
Now, moving on. 
300 minutes= 5 hours and 360 minutes= 6 hours
Now we know, he traveled a total of 11 hours. Makes sense!
Now, the distance is same from A to B and from B to A.
Keeping that in mind & our formula, D= s*t
B to A, D= 60*t (either 5 hours/6 hours) 
and from A to B= 50*t should be equal.
So, logically, from B to A= 60*5= 300 and from A to B= 50*6=300
We needed the time from B to A, which is 5 hours, i.e 300 minutes.
Answer is D.

kiranbhasker · Answer

Given: Distance is constant.
Total time taken = 11 hrs, avg speed A to B = 50, avg speed B to A = 60

avg speed = total D/ total time taken.

Let time for A to B = x
and time from B to A = 11-x

Avg speed A to B = 50 m/hr = D/x---- (1)
Avg speed B to A = 60 m/hr = D/11-x (2)

equating 1 and 2 
 D = 50*x =60*(11-x)
simplifying 110x = 660 
=> x = 6 ,Question asks time from B to A, therefore 11-6 = 5.
5*60 =  300

Fdambro294 · Answer

When the Distance is in equal parts (such as in a Round-Trip) the Average Speed will be equal = Harmonic Mean of the 2 Speeds driven over the Equal Distance Parts

Let Average Speed = b

Let a = 50 m/h from City A to City B

Let c = 60 m/h from City B to City A

Avg. Speed = b = (2 * a * c) / (a + c)

Avg. Speed = 2 * 50 * 60 / (50 + 60)

Avg. Speed = 600/11 miles per hour

The General Average Speed Formula = (Total Distance traveled) / (Total Time Taken)

Since it is a Round-Trip and each part of the trip has equal Distance, Let 1 Part of the Trip = d

Avg. Speed = 600/11 m.p.h. = 2 * d / 11 hours

d = 300 miles = Distance from City A to City B and vice-versa

Question: how many MINUTES did Alan take to drive from City B to City A (Return Trip)?

Time = Distance/Speed

T = 300 miles / 60 m.p.h. = 5 hours

5 hours * (60 min. / 1 hour) = 300 minutes

Answer D

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Alan drove from city A to city B at an average speed of

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