A car traveled 65% of the way from Town A to Town B at an average spee

Question

A car traveled 65% of the way from Town A to Town B at an average speed of 65 mph. 
The car traveled at an average speed of v mph for the remaining part of the trip. 
The average speed for the entire trip was 50 mph. What is v in mph?

(A) 65 
(B) 50 
(C) 45 
(D) 40 
(E) 35

Source: Nova's GMAT Math Prep

Kudos for nice answers.

DensetsuNo · Accepted Answer

My take: 
 Distance = Rate  x  Time

We will solve this problem as  \frac{D1}{R1} + \frac{D2}{R2} = \frac{Dtot}{Rtot}

Whenever we have a % as a distance, that percentage becomes our distance (since the real distance would be a multiple of it)
Therefore  D1=65   D2=35   Dtot=100 .

As for the rate we knew:  R1=65mph   R2=v   Rtot=50mph

Therefore  \frac{65}{65} + \frac{35}{v} = \frac{100}{50}  ->  1 + \frac{35}{v} = 2  ->  v = 35

Bunuel · Answer

Similar question to practice: a-car-traveled-75-of-the-way-from-town-a-to-town-b-at-an-149921.html

OptimusPrepJanielle · Answer

Assume total distance = 100miles

Time taken for 65 miles = 65/65 = 1 hour
Time taken for the rest of the 35 miles = 35/v hours.

Average speed = 50
Therefore the total time needed = 2 hours.

2 = 1 + 35/v
Hence v = 35 mph

Correct Option: E

Divyadisha · Answer

Let the total distance be x
.65x is travelled with speed 65 mph and .35x is travelled with speed v

Avg speed= total distance/total time
50= x/.65x/65+.35x/v
50= 1/.01+.35/v
50= v/.0v+.35
.5v + 17.5= v
v= 35 mph

E is the answer

chetan2u · Answer

Hi,
There can be two three ways..

1) choices-
When the distance covered is same at two different speeds A and B, the average speed is \frac{2AB}{A+B} ...

here let the second speed be x so average = \frac{2*x*65}{x+65}= 50 ................ 130x= 50x + 50*65............80x = 50*65 \approx{50*64}...............x = 40 ....
so, if the distance travelled was same, speed would be nearly 40....
But here distance travelled at 65 is 65% of total distance, so speed for lesser distance has to be less than 40..
ONLY 35 is in choice 
E

2) let the distance be 100 miles..
65% = 65 miles...
so time taken to travel  65 miles @ 65mph = \frac{65}{65}= 1 hr....
Total time takem =  100 miles @ 50mph = \frac{100}{50} =2 hr...
so the remaining 35% or 35 miles was travelled in 1 hour, so speed = 35/1 = 35mph

hasnain3047 · Answer

lats say total distance from A to B is 100 miles
65 miles is traveled by 65 miles/hour so it took 1 hour
100 miles is traveled by 50 miles/hour so it took 2 hours

so 35 miles distance is covered in 1 hour
hence v = 35/1 = 35 miles/hour

Answer is E

JeffTargetTestPrep · Answer

We can let the distance from Town A to Town B = 100 miles. So the car traveled the first 65 miles at 65 mph and the last 35 miles at v mph. Since total distance/total time = average rate, we have:

100/(65/65 + 35/v) = 50

100/(1 + 35/v) = 50

100 = 50(1 + 35/v)

2 = 1 + 35/v

1 = 35/v

v = 35

Answer: E

Hoozan · Answer

avigutman  please could you help me understand how we could use the number line approach or some other logic to solve the above question?

KarishmaB , I notice that the ratio of the distance is given to us. Could we use the ratio and solve? If yes, please could you how

KarishmaB · Answer

If I had 30 secs to answer this question, I would mark 35 and move on. 
65 mph is 15 more than 50 mph. If the car had travelled equal distances at speeds 35 mph and 65 mph, its average speed would have been a decent bit less than 50, the middle value (it would be about 45). But the car travelled 65% distance at the higher speed which means that its average would have become higher and 50 is certainly a good guess then.

But this is how we will solve it:
Since 65% distance is travelled at 65 mph, assume total distance is 100 miles. 
Average speed  = 50 = \frac{100}{\frac{65}{65} + \frac{35}{v}}

2 = 1 + \frac{35}{v}

v = 35 mph

Answer (E)

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A car traveled 65% of the way from Town A to Town B at an average spee

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