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v1,v2,v3 = 30,60,80
S1.
t1:t2:t3 = 3:2:1,3x,2x,x
dx = vx*tx = k.x
total d will also be p.x. t is also 6x, so solvable.
S2, we have d1:d2:d3,and vx, so we can fend ut ratio of t, solvable as above. answer (D)
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leg 1 distance = x km
leg 2 distance = y km
leg 3 distance = z km.

avg speed for 1 = 40 k /h
f0r 2 = 60 k/h
for 3 = 80 k/h

time for 1 = x/40
time for 2= y/60
time for 3 = z/80

avg speed for whole = distance / time

x+y+z / (x/40) + (y/60) + (z/80)

240 (x+y+z) / 6x+4y+3z

we need to find value of x,y,z to get the avg speed.

S-1

x/40 = 3p, x= 120p
y/60 = 2p, y = 120p
z/80 = p, z= 80p

now value of x,y,z is in P we can easily find the avg value as p get cancelled out in both numerator and denominator.
hence sufficient.

S-2
x= 3p
y= 3p
z= 2p

now this is also sufficient as the same we discussed in above statement.
hence sufficient.

choice D


Bunuel
A courier traveled from Hillford to Lakeshore in three consecutive legs, with no stops between the legs. On the first leg, the courier’s average (arithmetic mean) speed was 40 kilometers per hour; on the second leg, the courier’s average (arithmetic mean) speed was 60 kilometers per hour; and on the third leg, the courier’s average (arithmetic mean) speed was 80 kilometers per hour. What was the courier’s average speed for the entire trip?

(1) The ratio of the times the courier spent on the first, second, and third legs, respectively, was 3:2:1.

(2) The ratio of the lengths of the first, second, and third legs, respectively, was 3:3:2.


 


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HF |---------------------|-----------------------------|------------------------| LS
|-----40km/h-------|----------60km/h-----------|--------80km/h-------|
|-------t1------------|-----------t2----------------|---------t3------------|
|-------x1------------|-----------x2---------------|----------x3-----------|

Avg speed=Total distance/ Total time taken=?

Evaluating statement 1 alone,
t1:t2:t3= 3:2:1
.: Total time taken is=3t+2t+t=6t
.: Total distance travelled= (40*3t)+(60*2t)+(80*t)
.: We can find out the average speed. Since in the numerator & denominator t will get cancelled out.

.: St. 1 is sufficient alone, i.e., A or D option is available.

Evaluating St. 2 alone,
.: x1: x2: x3=3:3:2
.: Total distance covered=3x+3x+2x
.: Total time taken= (3x/40)+ (3x/60)+ (2x/80)
.: we can find out the avg speed. Since the x will get cancelled out from the denominator & numerator.

.: St. 2 alone is sufficient.

.: D is correct answer.

Bunuel
A courier traveled from Hillford to Lakeshore in three consecutive legs, with no stops between the legs. On the first leg, the courier’s average (arithmetic mean) speed was 40 kilometers per hour; on the second leg, the courier’s average (arithmetic mean) speed was 60 kilometers per hour; and on the third leg, the courier’s average (arithmetic mean) speed was 80 kilometers per hour. What was the courier’s average speed for the entire trip?

(1) The ratio of the times the courier spent on the first, second, and third legs, respectively, was 3:2:1.

(2) The ratio of the lengths of the first, second, and third legs, respectively, was 3:3:2.


 


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Statement 1 - ift the ratio of times is 3:2:1, we can set them to 3t, 2t, and t then multiply by the distances.

40(3t) = 120t, 60(2t) = 120t, 80t

120+120+80 = 320t for distance with a total time of 6t (3+2+1). Average speed is 320t/6t =160/3. sufficient

Statement 2

If we let distances be 3x, 3x, and 3x, the times it take would be 3x/40, 3x/60, and 3x/80 or distance/speed. The sum of these times = 3x/20.

Total distance would be 8x (3+3+2) and total time = 3x/20

Average speed = distance/time =8x/ (3x/20) = 160/3. sufficient.

D. Each statement alone is sufficient.
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Ans Choice D: Given Leg1 avg speed = 40kmph ; Leg2 avg speed = 60kmph ; Leg3 avg speed = 80kmph.
Avg speed of entire trip = Total distance / Total time

Stmt 1: Ratio of time t1 : t2 : t3 = 3 : 2 : 1
Therefore, t1 = 3k ; t2 = 2k; t3 =k and distance d1=40x3k = 120k. Similarly, d2 = 120k , d3= 80k
Avg speed = (120k+120k+80K)/(3k+2k+k) = 320/6 kmph (Sufficient)

Stmt 2: Ratio of legs d1 : d2 : d3 = 3 : 3 : 2 = 3k : 3k : 2k
t1= d1/s1 =3k/40; t2 = d2/s2 = 3k/60; t3=d3/s3 = 2k/80
Avg speed = (3k+3k+2k) / (3k/40 + 3k/60 + 2k/80) = 320/6 kmph (Sufficient)
Bunuel
A courier traveled from Hillford to Lakeshore in three consecutive legs, with no stops between the legs. On the first leg, the courier’s average (arithmetic mean) speed was 40 kilometers per hour; on the second leg, the courier’s average (arithmetic mean) speed was 60 kilometers per hour; and on the third leg, the courier’s average (arithmetic mean) speed was 80 kilometers per hour. What was the courier’s average speed for the entire trip?

(1) The ratio of the times the courier spent on the first, second, and third legs, respectively, was 3:2:1.

(2) The ratio of the lengths of the first, second, and third legs, respectively, was 3:3:2.


 


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1) Let the times for the 3 legs be 3t, 2t and t
Distances = 40(3t), 60(2t), 80(t) = 120t, 120t, 80t
Total distance = 320t
Total time = 6t
Avg speed = 320t/6t = 160/3 km/hr
Sufficient

2) Let the distances be 3d, 3d and 2d
Times = 3d/40, 3d/60 and 2d/80
Total time= 3d/40 + 3d/60 + 2d/80 = 3d/20
Total distance = 8d
Avg Speed = 8d/(3d/20) = 160/3 km/hr
Sufficient

Ans : D
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<-----x----><------y------><-------z------>
Speeds= 40 -----60-----80

we need to find avg of whole trip xyz which is total distance/total time =?

1) tx: ty: tz = 3:2:1 = 3a:2a:1a
now we can find total distance/ total time = (120a + 120a+ 80a)/6a
Sufficient.

2) here we know Dx: Dy: Dz= 3a:3a:2a
so tx= 3a/40, ty=3a/60, tz=2a/80
So now we can find total distance/total time = 8a / (3a/40 + 3a/60 + 2a/80)
Sufficient.

So the answer is D
Bunuel
A courier traveled from Hillford to Lakeshore in three consecutive legs, with no stops between the legs. On the first leg, the courier’s average (arithmetic mean) speed was 40 kilometers per hour; on the second leg, the courier’s average (arithmetic mean) speed was 60 kilometers per hour; and on the third leg, the courier’s average (arithmetic mean) speed was 80 kilometers per hour. What was the courier’s average speed for the entire trip?

(1) The ratio of the times the courier spent on the first, second, and third legs, respectively, was 3:2:1.

(2) The ratio of the lengths of the first, second, and third legs, respectively, was 3:3:2.


 


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Bunuel
A courier traveled from Hillford to Lakeshore in three consecutive legs, with no stops between the legs. On the first leg, the courier’s average (arithmetic mean) speed was 40 kilometers per hour; on the second leg, the courier’s average (arithmetic mean) speed was 60 kilometers per hour; and on the third leg, the courier’s average (arithmetic mean) speed was 80 kilometers per hour. What was the courier’s average speed for the entire trip?

(1) The ratio of the times the courier spent on the first, second, and third legs, respectively, was 3:2:1.

(2) The ratio of the lengths of the first, second, and third legs, respectively, was 3:3:2.


 


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total avg speed = total dis/total time
for (1) ---> total dis = 40*3x+60*2x+80*x, total time = 6x
so (1) alone is sufficient.

for (2)---> total dis = 8x, total time = 3x/40 + ....it will contain x which will cancel out. thus, (2) is sufficient.
Therefore, Option D both are alone sufficient.
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Based on the information provided we just need enough information to get total time or distance and we can solve the question
S1 Ratio is 3x:2x and x. Total time is 3x+2x+x= 6x while total distance is 40x3x=120x+(60x2x)+(80x)= 320x
Average speed 320x/6x= 531/3km/hr hence sufficient
S2 Ratio 3y:3y:2y= 8y
Time for each lag 3y/40, 3y/60, 2y/80. Average speed 8y/(3y/20)= 531/3km/hr hence sufficient
Ans D
Bunuel
A courier traveled from Hillford to Lakeshore in three consecutive legs, with no stops between the legs. On the first leg, the courier’s average (arithmetic mean) speed was 40 kilometers per hour; on the second leg, the courier’s average (arithmetic mean) speed was 60 kilometers per hour; and on the third leg, the courier’s average (arithmetic mean) speed was 80 kilometers per hour. What was the courier’s average speed for the entire trip?

(1) The ratio of the times the courier spent on the first, second, and third legs, respectively, was 3:2:1.

(2) The ratio of the lengths of the first, second, and third legs, respectively, was 3:3:2.


 


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So we are given, L1= 40 kmph; L2 = 60 kmph; L3 = 80 kmph.
We need to calculate average speed of entire trip = Total Distance / Total Time

S1: The ratio of the times the courier spent on the first, second, and third legs, respectively, was 3:2:1. S = D / T
So, D1 = 40*3x = 120x; D2 = 60*2x = 120x; D3 = 80x
Total Distance = 320x; Total Time = 6x

S2: The ration of length of first, second, and third legs, respectively, was 3:3:2
D1 = 3d, D2 = 3d, and D3: 2d. So total distance = 8d
T1 = 3d / 40, T2 = 3d / 60; and T3 = 2d / 80, Total Time = T1+T2+T3
So we can calculate average Speed.

So both the statements, individually, sufficient.
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From statement 1, we get:- total time for 3 legs= 3x+2x+1x
average speed= total distance/ total time = 320x/6x
statement 1 alone is sufficient

From statement 2, we get:- total distance for 3 legs= 3y+3y+2y
average speed= 8y/ (26y/240)

statement 2 alone is sufficient
Bunuel
A courier traveled from Hillford to Lakeshore in three consecutive legs, with no stops between the legs. On the first leg, the courier’s average (arithmetic mean) speed was 40 kilometers per hour; on the second leg, the courier’s average (arithmetic mean) speed was 60 kilometers per hour; and on the third leg, the courier’s average (arithmetic mean) speed was 80 kilometers per hour. What was the courier’s average speed for the entire trip?

(1) The ratio of the times the courier spent on the first, second, and third legs, respectively, was 3:2:1.

(2) The ratio of the lengths of the first, second, and third legs, respectively, was 3:3:2.


 


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...................Speed.............Time..............Distance
1................. 40......................t1 ................40t1
2................. 60....................t2 ..................60t2
3................. 80 .....................t3 ................ 80t3

Average speed = Total distance/ Total time

1) Ration of times= 3:2:1 or
t1=3x ; t2=2x ; t3=1x
Average speed= (120x+120x+80x)/6x =320x/6x =160/3
It is sufficient

2) ratio of distance= 3:3:2
t1= 3x/40 ; t2=3x/60; t3=2x/80
Total time= t1+t2+t3 = 3x/20
Average speed= 160/3
It is sufficient

D. Each statement alone is sufficient
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If times are known proportionally use weighted average, which will be the same throughout any figures. Hence A is sufficient. If distances are known proportionally - use weighted mean. Hence B is also sufficient on its own. I plugged in numbers and got the same values. Hence D is our answer.
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R (total) = D (total) / T (total)
R=rate
D=distance
T=time

R1=40, R2=60, R3=80
R(total) =?

Statement 1 - T1:T2:T3 = 3:2:1

By knowing the ratio of T, we can calculate:
D (total) = RT-1 + RT-2 + RT-3 with T=x
=40(3x) + 60(2x) + x = 320x

T (total) = 3x + 2x + x = 6x

R (total) = 320x / 6x = 320/6

1. Sufficient

Statement 2 - D1 : D2: D3 = 3:3:2

By knowing the ratio of D, we can calculate
T (total) = D/R (1) + D/R (2) + D/R (3) with D=x
= 3x/40 + 3x/60 + 2x/80
= 36x/240

D (total) = 3x + 3x + 2x = 8x

R (total) = D/T (total) = 8x / 36x * 240 = 2/9*240

2. Sufficient

So, the answer is D.
Bunuel
A courier traveled from Hillford to Lakeshore in three consecutive legs, with no stops between the legs. On the first leg, the courier’s average (arithmetic mean) speed was 40 kilometers per hour; on the second leg, the courier’s average (arithmetic mean) speed was 60 kilometers per hour; and on the third leg, the courier’s average (arithmetic mean) speed was 80 kilometers per hour. What was the courier’s average speed for the entire trip?

(1) The ratio of the times the courier spent on the first, second, and third legs, respectively, was 3:2:1.

(2) The ratio of the lengths of the first, second, and third legs, respectively, was 3:3:2.


 


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Courier -> Hillford to Lakeshore -> In 3 legs
First Leg courier average speed S1= 40 km/hr
Second leg courier avg speed S2 = 60km/hr
Third leg courier avg speed S3 = 80km/hr

We need to find avg speed (S) for entire trip

Statement 1 ->

Let the times in the first leg,second leg and third leg given be 3t, 2t and t

Distance travelled in first leg = 40*3t = 120t
Distance travelled in second leg = 60*2t = 120t
Distance travelled in the third leg = 80*t = 80t

Average speed = Total distance/ Total time = 120t + 120t + 80t / 3t+2t+t = 160/3

Statement 1 is sufficient

Statement 2 ->

Let the distance travelled in the first leg, second leg and third leg given be 3x, 3x and 2x

Time taken in first leg = 3x/40
Time taken in second leg = 3x/60 = x/20
Time taken in third leg = 2x / 80 = x/40

Average speed = Total distance/Total Time = 3x+3x+2x / (3x/40 + x/20 + x/40) = 160/3

Statement 2 is sufficient

D. Each statement is sufficient
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Did this one by Average speed = total distn / total time
Note that the speed of three legs is fixed
Now we need distance and time info, ratios will work too as the variable might get cut in denominator

A alone - take times as 3t, 2t, t
So Avg speed = total distn/ 6t
Distn can be written by speed*time for each leg and that t variable will get cut
So sufficient

Now B alone ,distance can be taken as 3d, 3d, 2d and for denominator in total time - replace time by dist/speed so again distan variable will get cancelled
Hence B alone sufficient too

Thus D
Bunuel
A courier traveled from Hillford to Lakeshore in three consecutive legs, with no stops between the legs. On the first leg, the courier’s average (arithmetic mean) speed was 40 kilometers per hour; on the second leg, the courier’s average (arithmetic mean) speed was 60 kilometers per hour; and on the third leg, the courier’s average (arithmetic mean) speed was 80 kilometers per hour. What was the courier’s average speed for the entire trip?

(1) The ratio of the times the courier spent on the first, second, and third legs, respectively, was 3:2:1.

(2) The ratio of the lengths of the first, second, and third legs, respectively, was 3:3:2.


 


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Average Speed = Total Distance/Total Time

We are given that leg 1 = Speed -40
Leg 2 = speed 60
Leg 3 = Speed - 80

Statement 1 => Ratio of time is given as 3:2:1

Considering the above ratio, we can find average as 40(3)x+ 60(2)x+ 80(1)x/(6x) = 160/3

hence, this statement is sufficient

Statement 2 => Ratio of lengths of legs is 3:2:1
Lengths = distance

Since we have both speed and distance, we can express time in terms of speed and distance and get the average as below:

Average = 6y/((3y/40)+(2y/40)+(1y/40)) = 160/3

This Statement is also sufficient

Hence the answer is Option D
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