Divs bicycle tour consists of three legs of equal length. For the fi

\(24 = \frac{3*16*24*X}{16*24+ 24*X+X*16}\)

\(16*24= 8X\)

\(X=48\)


** remember if distance is same the average speed is harmonic mean of speeds of each leg. in this case harmonicmean of 16,24 and X .
** also remember that if time taken is same for each leg then the average speed is Arithmeticmean of speeds of each leg.

Answer E.

So let each leg be \(l km\). let x km/hour be speed in last leg. Then for average speed to be equal to 24 km/hour following equation must hold.

\(\frac{l}{16} +\frac{l}{24} +\frac{l}{x} = \frac{3l}{24}\)

Solving further,

\(1/16 + 1/24 +1/x = 1/8\)
\(1/2+1/3+8/x = 1\)
\(8/x = 1/6\)
\(x=48\)

Hi All,

While much of the work that is involved in this prompt is calculation-based (using the Distance Formula), the distance IS a variable, so we can TEST VALUES to get to the correct answer.

We're told that each "leg" of a bicycle tour is the same distance and the speed on each of the legs is 16km/hr, 24km/hr and X km/hr. We're asked what that third speed much be to make the AVERAGE SPEED for the ENTIRE tour 24km/hr.

IF....
Each leg = 24km

The ENTIRE tour is 72 km; an average speed of 24km/hr means that the entire tripe must be...

72km = (24km/hr)(Total Time)
72/24 = Total Time
3 hours = Total Time

1st leg --> 24km = (16km/hr)(T)
24/16 = T
1.5 hours = T

2nd leg --> 24km = (24km/hr)(T)
24/24 = T
1 hour = T

With 2.5 hours spend on the first two legs of the tour, this gives us 1/2 hour for the final leg of the tour:

3rd leg --> 24km = (X km/hr)(1/2 hour)
24/(1/2) = X
48 km/hr = X

So the speed of the 3rd leg must be 48 km/hr.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Lets pick a smart number for the distance of each leg = 48 kilometres (easy to compute since we have 16 and 24 as rates)

Using the RTD table, Lets substitute the known values

First leg --> 16 * T = 48 ==> T = 3 hours
Second leg --> 24 * T = 48 ==> T = 2 hours

We need to calculate the time taken to cover the entire trip averaging 24 km/hr (from question stem)
Since the distance for all 3 legs are the same, distance for the whole trip = 48 + 48 + 48 = 144

Using RTD, 24 * T = 144 ==> Total time = 6 hours averaging 24 km/hr the whole trip

He already took 5 hours in the first two legs combined. Therefore, he needs to travel the third leg in 1 hour to make up for the lost time.

So this informs us that we need to find the Div's speed in the last leg in such a way that he covers the 48 kilometers in 1 hour. ( i.e. )

R * 1 = 48 ==> 48 kms/hr

Hence, Answer E

Answer=E
Average Speed=Total Distance Traveled/Total Time taken
Let total distance=d and speed in final leg=x
d/(d/48+d/72+d/3x) =24
Solving for X=48

I don't know whether this approach is right , I found the answer using below mentioned method

d/16 + d/24 + d/x = 3d/24 ( since given 3 equal distance and overall average speed is 24)

now take lcm of 16 and 24 = 48

consider d = 48

48/16 + 48/24 + 48/x = 48*3 / 24

3 + 2+ 48/x = 6

Therefore x = 48 which will make the LHS = RHS.

Hence Answer Choice is E.

Hi monk16,

Yes, your approach IS correct - you're essentially just organizing the information in a different way. You'll come to find that certain question on Test Day will be easier/faster for you DEPENDING on how you choose to 'set up' your work. As such, some of your study time should be spent practicing other ways to approach a given prompt, other ways to perform the necessary calculations, converting information from one format to another, etc. You'll be far better able to handle the variety of questions that you'll face on the Official GMAT if you have a variety of approaches at your disposal.

GMAT assassins aren't born, they're made,
Rich

I took a lot of time figuring out that without distance how this problem can be solved , since time is also a variable.
Then i went through the solutions and found it relatively easy.
Thanks

Little bit of attention may save you time..though I took sometime to figure this one out..it may be useful for future..

Now pay attention...

We have 3 legs of equal length in total

A---------B----------C----------D

Legs and average speeds
AB 16
BC 24
CD x

Overall 24

Now, notice that BC already has an average of 24, which is our target overall average speed. If the average speed of the remaining two legs is 24, then what will we have as our final average?...24

So instead of finding average of three legs..we'll do it for two only.

\(24 = \frac{2*x*16}{x+16}\)

solving for x gives out x = 48 (E)

(leg2-leg1)+leg2=leg3
(24-16)+24=32
(16+24+32)/3=24
32

Bunuel wrote:
Div’s bicycle tour consists of three legs of equal length. For the first leg Div averaged 16 kilometers per hour. For the second leg he averaged 24 kilometers per hour. What speed must Div average for the final leg in order to average 24 kilometers per hour for the entire tour?

A) 20 kilometers per hour
B) 28 kilometers per hour
C) 32 kilometers per hour
D) 40 kilometers per hour
E) 48 kilometers per hour


Since no absolute value of distance is given, this is the type of problem which can be solved with a minimum of calculation by assuming a suitable numerical value for distance [which, in this case, is 48 kmph for each leg, 48 being the LCM of 16 and 24].
Average Speed=[Total distance/Total time]
Thus, 24=[48x3]/T [T being the Total time]
T/4, T=6 hrs
Since Dev took 3 hrs [48/16] for the 1st leg and 2 hrs [48/24] for the 2nd, he has only 1 hr to complete the 3rd leg. T/4, he must average 48 kmph on the final leg if he is to average 24 kmph for the entire trip.
Ans: E
P.S. You can assume any numerical value for the distance and arrive at the correct answer but the calculations would be more complicated and time-consuming.

hey EMPOWERgmatRichC
I did it as follows
let d = 1 for each lap
avg speed=total d/total time
total time = 1/16+1/24+1/x= 6x+48/48x
24=3*48x/6x+48
after simplification im getting
6x=6x+48
could you help me with what am i doing wrong?

Hi Kritisood,

You're correct that the common denominator of (1/16), (1/24) and (1/X) is 48X.... but you made a small error on the next step. You shouldn't end up with (6X + 48).... you should end up with (5X + 48). Since you didn't show all of your steps, I'm guessing that you accidentally 'converted' (1/16) into (4X/48X) when it should have been (3X/48X).

GMAT assassins aren't born, they're made,
Rich

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