GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight

­

 
Distance = 100 miles
Time = 10 hours
Average Speed = 10 miles/hr


Average speed =            \(\frac{X + Y }{2}\)         or        \(\frac{2XY}{X + Y}\)


\(\frac{X + Y }{ 2} = 10\)             or               \(\frac{2XY}{X + Y}  =  10 \)


The only two values that satisfy the above equations are x = 10 and y = 10

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Since it covers 100 miles in 10 hours, it follows that for the first 5 hours, it travels with speed x, and for the next 5 hours, it travels with speed y.

5x + 5y = 100
x + y = 20

Since x > y or x = y, only x = y = 10 satisfy among the given choices.

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­x mph for 5 hr = 5x
y mph for 5 hr = 5y

total 5x + 5y = 100 miles
x + y = 20

given x>=y,

so x >=10 and y <= 10

hence, the only feasible option is both 10 mph.

­total time = 10
total distance = 100

x>=y

5x+5y=100
x+y=20

The only possible values are x=10 and y=10

50 miles is covered in the both the speeds

Total time= 10

t1+t2=10
50/x+50/y=10

5/x+5/y=1

So if x=10 then 

50/10+ 50/y=10
y=10

So x=10, y=10 

Ans is x=10, y=10
 

The car travels travels at x mph for 5 hours and y mph for 5 hours to complete 100 miles. 
­\(5*x+5*y=100\)
­\(x+y=20\)
The only options that make sense are x=10 mph and y=10 mph. ­

­

­5x+5y =100
5(x+y)=100
x+y=20

and as it's given that x>=y. Then, x=y=10 mph is the best-suited option.

Given  the speed for 1st Half Time(i.e 5 hrs) Speed = x mph
Given  the speed for 2nd Half Time(i.e 5 hrs) Speed = y mph

­S=D/T

x=D1/5 and y=D2/5

Given Total Distance =100 miles = D1+D2
100=5x+5y
x+y=20

The option that fits the condition is if x=10mph and y=10mph

 

 
Given, x*5 + y*5 = 100.

x + y = 20.

Also, x>=y

The only values consistent with this are, x=10, and y=10.

­Total duration: 10 hrs
Total distance: 100 miles

Speed for half of the travel duration: x mph
Speed for the remaining half of the travel duration: y mph

also, x >= y

Distance covered when vehicle running at x mph = 5x miles
Distance covered when vehicle running at y mph = 5y miles

5x + 5y = 100
x+y = 20

As per the given option, the scenario is only possible when both x and y are 10 mph.
x: 10
y: 10

Given
Total distance covered=100 miles
Total time =10 hour
X>=Y
"Exactly one half of the travel time"= 10/5

Resulting Equation-
Speed*Time=Distance
X*5+Y*5=100
X+Y=20

Check options :

Possible - X=3,5,7,10,20
Possible - Y=3,5,7,10

Out of the given options, only relevant option is 10.

Hence X=Y=10 MPH

­
­The total distance equals \(0.5t*x + 0.5t*y = 100\)
And \(t = 10\), so \(0.5t = 5\)
Then, \(100 = 5x + 5y\)
And \(20 = x + y\)

From the answer options, the only suitable options are: both x=10 and y=10.­­

5x+5y=100
x+y=20
x>=y
x=10;y=10­

5x + 5y =100
x +y =20
Out of the options only 10,10 will only satisfy

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­Here we are.
At the finish.
We need a miracle to win this competition.
But we gave whatever we could.
For the last time, here is my explanation:

Glance - the Question&Answer Choices:
Question: We are dealing here with Rates (*Time=Distance) question.
Answer Choices: They do not help us guess or estimate because the answers we are looking for are jointly consistent.

Rephrase - Reading and Understanding the question:
Given: Okay, let’s collect what we have here:
Distance = 100 miles
Time = 10 hours
First Half of the time:   x*5
Other Half is: y*5 
x greater or EQUAL to y  (Pay attention to the "equal" here)
[?]: Finding x and y.
We can find them by setting mathematical equation of R*T=D:
The equation 5x + 5y = 100 

Solve:
We have an equation 5x + 5y = 100, which means x + y = 20.
The only possible answers that fit here are 10 and 10.
The answers are 10 and 10.



THE END
I hope you liked the explanation; I did my best here.
Please let me know if you have any further questions about this question or my explanation.