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605-655 (Medium)|   Math Related|         
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Abhijeet24
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 09:10
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Bunuel
­An athlete training for a cross-country race covered three types of terrain in three distinct segments of a practice run; she ran across stretches of packed dirt, rocky scree, and grass, in that order. On packed dirt, she ran at an average speed of 201 meters per minute; she then rapidly slowed on the rocky scree, and covered the grass segment at an average speed of 100.5 meters per minute. The distance she covered on grass was four times the distance she covered on packed dirt, and it took her 21 minutes to cover both. On the table, select the distance she covered on both these terrains, in meters. Make only two selections, one in each column.


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­Let the distance covered in packed dirt be d, then the distance travelled in grass would be 4d.
The equation becomes:
d/201 + 4d/101.5 = 21
d/201 + 8d/201 = 21
9d/201 = 21
d = 21 * 201/9 = 469

solving this to get d= 469 and 4d = 1876

Distance covered on packed dirt (meters) = 469 
Distance covered on grass (meters) = 1876
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 09:31
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Lets consider Dp distance covered on packed dirt and TD time for to cover the packed dirt
Lets consider Dg distance covered on Grass and TG time for to cover the Grass

We have
TD+TG =21 (min)(*)
Dg=4Dp (**)

Then

201-->1min
dp=Dp/201

Also

100.5-->100.5
Dg-->Dg/100.5

Then, from (*)
we have : 21=Dp/201 + Dg/100.5
=>21=0.5Dp/100.5 + Dg/100.5
=>21=4.5 Dp/100.5
=>Dp=21*100.5/4.5= 469

and from (**)
we conclude that Dg=4*469 =1876
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 09:40
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­Let the distance covered on dirt be x
Dist. Covered on grass will be 4x

Time = Distance / Speed
 Speed on grass = 100.5 m/min  and speed on dirt 201 m/min

Time on grass + Time on Dirt = Total time (21 min given)

4x / 100.5 + x/ 201 = 21
solving this equation we get the value of dirt as 469 m and the value of grass as 1879m
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 09:42
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­               PD                    RS                   G
-----------------------------------------------------------------
dist         d (m)                                     4d (m)
-----------------------------------------------------------------
speed  201 (m/min)    <201(m/min)    100.5(m/min)
​​​​​​​-----------------------------------------------------------------

d/201 + 4d/100.5 = 21 min

d = 469m

4d = 1876m
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 09:56
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Dirt - 469
Grass- 1876

Given
Grass = speed= 100.5 = 201/2, Distance (dg)= 4x
Dirt = 201, Distance (dr)= x

so
(4x/100.5) + (x/201) = 21

solving we get
X= 469 = dirt
4X= 1876 = grass
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 09:58
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My answer:-
Distance covered on packed dirt (meters) :- 469
Distance covered on grass (meters) :- 1,876
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 10:02
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Okay, we're almost at the end.
I will miss this competition, for sure.
The orange team looks invincible but we will fight until the end.
Let's start with our explanation of this topic:

Glance - the Question&Answer Choices:
Question: We have here a word problem. kind of R*T=D.
Answer Choices: We can see they are far away from each other. we can estimate here.

Rephrase - Reading and Understanding the question:
Given:
3 routes:
                     --------------------------|---------------------------|----------------------------
Rate:                201 meters/mins                                         100.5 meters/mins
Distance:                     D                                                              4D                         
Time:              her total time was 21 mins.

[?]: what is the distance of each of the 2 routes.

Solve:
Ok so we can come up with an equation here:
[D][/201] + [4D][/100.5] = 21mins
D + 8D = 21 * 201
9D = 3*7*3*67   /:9
D = 7*67 = 469
alright so we know D = 469.
We can calculate each routes (So We have our answer):
Packed dirt = D = 469
Grass = 4D = 1876


THE END
I hope you liked the explanation, I have tried my best here.
Let me know if you have any questions about this question or my explanation.
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 10:02
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An athlete training for a cross-country race covered three types of terrain in three distinct segments of a practice run; she ran across stretches of packed dirt (PD), rocky scree, and grass, in that order. On packed dirt, she ran at an average speed of 201 meters per minute; she then rapidly slowed on the rocky scree, and covered the grass (G) segment at an average speed of 100.5 meters per minute. The distance she covered on grass was four times the distance she covered on packed dirt, and it took her 21 minutes to cover both. On the table, select the distance she covered on both these terrains, in meters. Make only two selections, one in each column.

To cover 4 times the distance as PD, athlete will take 8 times the time taken on PD since speed on G is half
8x+x=21
x=21/9=2.3

Distance covered on PD=201*2.3= approx 460
Thus dist covered on grass= 4*460=1840

The closest choices are 469 and 1876

Ans D, B
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 10:08
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­Distance covered on packed dirt (meters): 469
Distance covered on grass (meters): 1876
It took her 8 times longer to cross the grass sections, because it is four times longer and she is twice as slow as on the packed dirt, so the 21minutes are divided into a ratio dirt/grass of 1:8
1 corrsponds to 2min20 and this times the 201m is equivalent to 469
8times 100,5M is equivalent to 1876m, which is four times as much as 469
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 10:30
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Bunuel
­An athlete training for a cross-country race covered three types of terrain in three distinct segments of a practice run; she ran across stretches of packed dirt, rocky scree, and grass, in that order. On packed dirt, she ran at an average speed of 201 meters per minute; she then rapidly slowed on the rocky scree, and covered the grass segment at an average speed of 100.5 meters per minute. The distance she covered on grass was four times the distance she covered on packed dirt, and it took her 21 minutes to cover both. On the table, select the distance she covered on both these terrains, in meters. Make only two selections, one in each column.


­
 


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Equation: ­dx/201 + dy/100.5 = 21
Given: dy = 4dx
...solving for dx = 469
dy = 4*469 = 1,876
 
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 10:32
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Bunuel
­An athlete training for a cross-country race covered three types of terrain in three distinct segments of a practice run; she ran across stretches of packed dirt, rocky scree, and grass, in that order. On packed dirt, she ran at an average speed of 201 meters per minute; she then rapidly slowed on the rocky scree, and covered the grass segment at an average speed of 100.5 meters per minute. The distance she covered on grass was four times the distance she covered on packed dirt, and it took her 21 minutes to cover both. On the table, select the distance she covered on both these terrains, in meters. Make only two selections, one in each column.


­
 


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­
Show more
­distance (dirt) / (speed) 201 + distance (grass) /100.5 = 21 (joint time)
given, dg = 4dd
solved for dd = 469
dg = 4*469 = 1,876
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 11:05
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Given - ­An athlete training for a cross-country race covered three types of terrain in three distinct segments of a practice run;
she ran across stretches of packed dirt, rocky scree, and grass, in that order.
On packed dirt, she ran at an average speed of 201 meters per minute; she then rapidly slowed on the rocky scree,
and covered the grass segment at an average speed of 100.5 meters per minute.
The distance she covered on grass was four times the distance she covered on packed dirt, and it took her 21 minutes to cover both.

To find -  the distance she covered on both these terrains, in meters.
\(Speed = \frac{Distance}{Time}\)­
 Therefore, \(Time = \frac{Distance}{Speed}\)it took her 21 minutes to cover both.
Time for dirt + Time for grass = 21
Lets assume the d as amount of distance covered in dirt stretch So, grass stretch equals = 4d
\(\frac{d}{201} + \frac{4d}{100.5} = 21\)­
\(\frac{d}{201} + \frac{8d}{201} = 21\)­
\(\frac{9d}{201} = 21\)­
\(d=469 meters.\)

Therefore, Distance covered on packed dirt (meters) = d = 469 meters Option B.
and Distance covered on grass (meters) = 4d = 4*469 = 1876 meters Option D.­
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 11:26
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Let's denote:
- d: Distance covered on packed dirt (meters)
- 4d: Distance covered on grass (meters) (since grass distance is four times packed dirt distance)

From the problem statement:
1. She covered both distances in a total of 21 minutes.
2. Speed on packed dirt = 201 meters per minute
3. Speed on grass = 100.5 meters per minute

We can set up the following equations based on time and distance:

For packed dirt:
d / 201

For grass:
4d / 100.5

Since the total time spent on both terrains is 21 minutes:
d / 201 + 4d / 100.5 = 21

Let's solve for d:

d / 201 + 4d / 100.5 = 21

To simplify, find a common denominator (which is 201):
d / 201 + 8d / 201 = 21
9d / 201 = 21

Multiply both sides by 201 to solve for d:
9d = 21 * 201
9d = 4221
d = 4221 / 9
d = 469

So, the distance covered on packed dirt is d = 469 meters.

Now, the distance covered on grass is 4d = 4 * 469 = 1876 meters.

Therefore, the distances covered are:
- Distance covered on packed dirt (meters): 469
- Distance covered on grass (meters): 1876­
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 12:32
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Packed dirt speed= P=201 meters per minute
Grass segment speed= G = 100.5 meters per minute
Distance she covered on grass= dg
Distance she covered on packed dirt= dp

The distance she covered on grass was four times the distance she covered on packed dirt

dg=4dp

and it took her 21 minutes to cover both (packed dirt and grass)
v=d/t
t=d/v
time she covered packed dirt=tp
time she covered gras= tg
21=tp+tg

since dg=4dp and d=vt
G*tg=4*(P*tp)
100.5*tg=4*(201*(21-tg))
100.5*tg=804*(21-tg)
100.5*tg=804*(21)-(804*tg)
100.5*tg+(804*tg)=804*(21)
904.5tg=16884
tg= 16884/904.5 =56/3

dg=G*tg= 100.5*(56/3)=1876mts
dg=1876mts
dg=4dp
1876mts=4*dp
dp=1874/4=
dp 469 mts

ANS
dg=1876mts
dp =469 mts

Distance she covered on grass= dg =1876mts
Distance she covered on packed dirt= dp=469 mts
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 12:52
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let ditance on dirt be X, so on grass 4X
(X/201)+(4X/100.5) = 21
(X/200)+(4X/100)=21
X=1400/3
X=1401/3  = 467....Nearest option 469

4x=4*469=1876

Answer 469 & 1876 ­
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 12:53
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­                      packed dirt                               rocky scree                               grass
speed                  201                                          100.5                                      Sg
distance                x                                               -                                          4x

Using the given information from the question, we can equate the total time taken by packed dirt and grass together to 21 minutes.
21 = (x/201) + (4x/Sg)

As 21 is the sum of x/201 and 4x/Sg, we can say x/201 has to be less than 21.
On that basis, we can easily eliminate the last 2 options.
Superfluous calculation:
If x=5,064, x/201= 25.19, which is greater than 21. Eliminate E.
If x=7,504, x/201= 37.33, which is greater than 21. Eliminate F.

Furthermore, if we observe closely, we can see that C=4A and D=4B
Therefore, x will either be A or B and 4x will either be C or D.
After these verbal eliminations, let's do a little, necessary, calculation.

A. Substituting x=316.5 in the above equation, we get Sg=65.16.
This is logically incorrect because speed on rougher rocky segment should be relatively ≤ speed on grass terrain.
Eliminate A.

We have our answers: x=option B and thus, 4x=option D.
Just to verify, let's calculate.
B. One more time, substituting x=469 in the above equation, we get Sg=100.
This is logically sound.

Distance covered on packed dirt (meters) = 469 i.e. option B
Distance covered on grass (meters) = 1876 i.e. option D
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 12:57
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­An athlete training for a cross-country race covered three types of terrain in three distinct segments of a practice run; she ran across stretches of packed dirt, rocky scree, and grass, in that order. On packed dirt, she ran at an average speed of 201 meters per minute; she then rapidly slowed on the rocky scree, and covered the grass segment at an average speed of 100.5 meters per minute. The distance she covered on grass was four times the distance she covered on packed dirt, and it took her 21 minutes to cover both. On the table, select the distance she covered on both these terrains, in meters. Make only two selections, one in each column.

Given:
Distance of dirt= D Speed on dirt = 201m/min
Distance on grass =4D Speed on grass = 100.5m/min
Time spent on both = 21min

Working:
Time= Distance/speed (for both grass and dirt)
21min = (D/201) + (4D/100.5)
9D=4221

D=469 = distance on the dirt
4D = 1876 distance on the grass
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 13:06
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Distance (PD) .......(x)= 201*t1
Distance (Grass) ..(4x)= 100.5*t2

t1+t2= 21
(x/201) + (4x/100.5) =21
x= 469...Distance (PD)

4x = 1876....Distance (Grass)
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 13:14
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Speed on packed dirt: 201 meters per minute.
Speed on grass: 100.5 meters per minute.
Distance on grass is 4 times the distance on packed dirt.
Total time for both segments: 21 minutes.
Let d be the distance on packed dirt (in meters). Distance on grass is 4d meters.
time on packed dirt= d/201
time on grass= 4d/100.5
total time = d/201+ 4d/100.5= 21
let's solve this equation to find d. => d=469
Distance on packed dirt: d=469 meters.
Distance on grass: 4×469=1 4d=4×469=1,876 meters.
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GMAT Club Olympics 2024 (Day 8): An athlete training for a cross-count 17 Jul 2024, 14:16
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Bunuel
­An athlete training for a cross-country race covered three types of terrain in three distinct segments of a practice run; she ran across stretches of packed dirt, rocky scree, and grass, in that order. On packed dirt, she ran at an average speed of 201 meters per minute; she then rapidly slowed on the rocky scree, and covered the grass segment at an average speed of 100.5 meters per minute. The distance she covered on grass was four times the distance she covered on packed dirt, and it took her 21 minutes to cover both. On the table, select the distance she covered on both these terrains, in meters. Make only two selections, one in each column.
 
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­There are 4 possible combinations that satisfy the distance ratio of 1 : 4.

1. 316.5m and 1266 m
Time taken to cover the dirt track = 1.57 min. 
Speed on rocky scree track = 66 metres/ min.

2. 469 m and 1876 m
Time taken to cover the dirt track = 2.3 min. 
Speed on rocky scree track = 104 metres/ min.

3. 1266m and 5064 m
Time taken to cover the dirt track = 6.35 min. 
Speed on rocky scree track = 361 metres/ min.

4. 1876m and 7504m
Time taken to cover the dirt track = 9.3 min. 
Speed on rocky scree track = 625 metres/ min.

considering the athlete rapidly slowed down for the scree track - only two options are possible - 1 and 2. Since option 2 is faster than her speed on grass, I chose option 1.



316.5 m and 1266 m
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