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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 06:58
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­A car is traveling on a straight stretch of a road at a constant rate of x mph, for exactly one half of the travel time. The remaining time, the car travels at a constant rate of y mph. The car does not stop and takes exactly 10 hours to complete the journey of 100 miles. It is also known that x is greater than or equal to y. Select values of x and y that are jointly consistent with the information provided. Make only two selections, one in each column.

 


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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 07:05
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­A car is traveling on a straight stretch of a road at a constant rate of x mph, for exactly one half of the travel time. The remaining time, the car travels at a constant rate of y mph. The car does not stop and takes exactly 10 hours to complete the journey of 100 miles. It is also known that x is greater than or equal to y. Select values of x and y that are jointly consistent with the information provided. Make only two selections, one in each column.

 


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GMAT Club Official Explanation:



Since the total time is 10 hours, and it is split into two equal halves, the car travels at speed x and speed y for 5 hours each.

The distance at x mph is 5x, and the distance at y mph is 5y. Thus, 5x + 5y = 100, which gives x + y = 20.

Out of all the options we have, the only two values that sum to 20 are 10 and 10. There is no other combination possible, and since x is greater than or equal to y, the answer is 10 + 10 = 20.­
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 07:14
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As we know total time * speed = distance traveled


5* speed x + 5* speed Y =100
So X+Y =20

So only 10,10 is feasible

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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 07:24
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10 miles per hour = x+ y , now x>= y so x has to be 7 y has to be 3
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 07:42
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A car is traveling on a straight stretch of a road at a constant rate of x mph, for exactly one half of the travel time. The remaining time, the car travels at a constant rate of y mph. The car does not stop and takes exactly 10 hours to complete the journey of 100 miles. It is also known that x is greater than or equal to y.

Select values of x and y that are jointly consistent with the information provided. Make only two selections, one in each column.

The car does not stop and takes exactly 10 hours to complete the journey of 100 miles. It is also known that x is greater than or equal to y.
x >= y
Total distance = 100 miles
Total time = 10 hours

A car is traveling on a straight stretch of a road at a constant rate of x mph, for exactly one half of the travel time.
Travel time = 5 hours
Speed = x mph 
Distance travelled = 5x miles

The remaining time, the car travels at a constant rate of y mph.
Travel time = 5 hours
Speed = y mph 
Distance travelled = 5y miles

Total distance travelled = 5x + 5y = 100 miles
x + y = 20 ; x >=y


xy
1010

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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 07:45
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Total miles 100 km travelled and total hours taken 10 hours so avg speed (X and Y speed)
speed is 100/10= 10 mph
now given that x>=y and from given option only fitted option is X=7mph and y=3mh hence X+Y= 10 mph
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 07:54
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Total journey is 100miles at 10 hours . Half of journey at xmph is 50miles and half at ymph is 50miles also. From the choices we can easily see that spped of 10mph =5hours in 50 miles. Hence both speeds is 1omph covering 50miles+50miles= 100 miles in 10 hrs

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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 07:55
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­A car is traveling on a straight stretch of a road at a constant rate of x mph, for exactly one half of the travel time. The remaining time, the car travels at a constant rate of y mph. The car does not stop and takes exactly 10 hours to complete the journey of 100 miles. It is also known that x is greater than or equal to y. Select values of x and y that are jointly consistent with the information provided. Make only two selections, one in each column.

total time is 10 hours
1st leg is 5 hours and 2nd leg is 5 houts
distance is 100 miles
5x+5y=100
x is greater than or equal to y
possible value of x,y is 10,10
10,10 is correct
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 08:04
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the half time = 5 hrs
=> 5x + 5y = 100
=>x+y = 20
And from the options, there is only one possibility, i.e., x = 10, y = 10.
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 08:06
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A car is traveling on a straight stretch of a road at a constant rate of x mph, for exactly one half of the travel time. The remaining time, the car travels at a constant rate of y mph. The car does not stop and takes exactly 10 hours to complete the journey of 100 miles. It is also known that x is greater than or equal to y. Select values of x and y that are jointly consistent with the information provided. Make only two selections, one in each column.­

Average speed = 100/10 = 10

So 10 = (x+y)/2 => x + y = 20

And x >= y

We have only one way from the options, i.e. 10 and 10. 

Hence answer is (10, 10)
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 08:07
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Bunuel
­A car is traveling on a straight stretch of a road at a constant rate of x mph, for exactly one half of the travel time. The remaining time, the car travels at a constant rate of y mph. The car does not stop and takes exactly 10 hours to complete the journey of 100 miles. It is also known that x is greater than or equal to y. Select values of x and y that are jointly consistent with the information provided. Make only two selections, one in each column.

 


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­The car does not stop and takes exactly 10 hours to complete the journey of 100 miles. The car averge speed = 100/10 = 10 mph.
And as x can be equal to y. Out of the options, x=y=10 mph.

Additionally, no other option can be right as other pair of answer would have x>10 and y<10 to maintain averge. but least value option greater than 10 is 20. and with 20 mph in 5 hrs, 100 miles get covered. So, no place for y. hence not possible.

So, the only answer would be x = y = 10 mph 
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 08:24
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let's consider T the total time of the journey, then :
x->1h
x.T/2 ->T/2

and
y-->1h
y.T/2->T/2

Since T=10
then : (x+y).T/2=100
(x+y).5 =100
x+y =20
from the values presented, and since x can be equal to y, the only solution that can be considered is x=y=10
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 08:28
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Given, car travels at x mhp for 5 hours and y mhp for 5 hours.
Also give x greater than or equal to y.

Lets try x as 20 mhp.
then distance tranvelled by x mhp = 20*5 = 100 miles.
then distance travelled at y mph will be 0. For that y has to be 0. since thats not an option x = 20 is not possible. 

Lets try x as 10 mhp.
then distance tranvelled by x mhp = 10*5 = 50 miles.
then distance travelled at y mph  = 100 - 50 = 50 miles. 
distance travleled at y mph = 5 * y = 50 miles
implies y = 10 mph.
 
and x greater than or equal to y.

Hence answer x & y = 10

 
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 08:32
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x+y=20
x=10
y=7­
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 08:33
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Bunuel
­A car is traveling on a straight stretch of a road at a constant rate of x mph, for exactly one half of the travel time. The remaining time, the car travels at a constant rate of y mph. The car does not stop and takes exactly 10 hours to complete the journey of 100 miles. It is also known that x is greater than or equal to y. Select values of x and y that are jointly consistent with the information provided. Make only two selections, one in each column.

 


This question was provided by GMAT Club
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­Let the total time of travel=t hours

According to question stem, for half of time i.e, t/2, car travels at a constant speed of x mph.
Therefore, distance travelled=x.t/2
and for another half of time, car travels at a constant speed of y mph.
Therefore,distance travelled=y.t/2

Adding both equations,we get,
xt/2+yt/2=100
 t/2(x+y)=100

Now, total time is given as 10 hours.

Substituting and solving, we get,
x+y=20
As x is greater than or equal to y,

Therefore, x=y=10 satisfies our condition.
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 08:36
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IMO
x=10
y=10

t=10 hours
d =100

100 = 5x+5y

20 = x+y

x>= y

x=y

x= 10; y=10
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 08:40
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Bunuel
­A car is traveling on a straight stretch of a road at a constant rate of x mph, for exactly one half of the travel time. The remaining time, the car travels at a constant rate of y mph. The car does not stop and takes exactly 10 hours to complete the journey of 100 miles. It is also known that x is greater than or equal to y. Select values of x and y that are jointly consistent with the information provided. Make only two selections, one in each column.

 


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­Since it takes 10h to complete the journey => half of the travel time = 1/2 x 10 = 5h 
We have distance = time x speed => 100 miles = 5x + 5y 
=> 5(x+y) = 100 => x + y = 20 and we know that x >=y => we can see in the options that only 10 + 10 = 20 and meet the criteria, the other answers cannot be added to 20 => choose 10 for x and 10 for y
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 08:40
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My answer is -
x = 10 and
y= 10
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 08:43
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x=y=10

Given
5(x)+5(y)=100
x+y=20

so, x>=y
given the option nothing adds up to 20
unless it is 10,10

so x=y=10
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GMAT Club Olympics 2024 (Day 10): A car is traveling on a straight 19 Jul 2024, 08:47
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­D=100
T=10
S1=xt1
S2=yt2
t/2=5
5x+5y=100
x+y=20
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