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19 Jul 2024, 13:19
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Given - 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 (Means half). The remaining time, the car travels at a constant rate of y mph.
The car does not stop and takes exactly 10 hours (Total time) to complete the journey of 100 miles (Total distatnce)
It is also known that x is greater than or equal to y. \(x≥y\)
Distance = Speed * time
Therefore, Distance traveled in first part of stretch of x mph = x*5 (5 is one half of total time 10Hrs)
Similarly, Distance traveled in later stretch of y mph = y*5
Total Distance = 100 miles
\(5x+5y = 100\)
Therefore,
\(x+y = 20\)
\(y=20 - x\)
and given \(x≥y\)
Therefore, now substituting y here.
\(x≥20-x\)
\(2x≥20\)
\(x≥10\)
now check for values from table, check for x=10,20,50
you will notice the only x=10 will satisfy based on given equation and will give you value of as y=10.
So both \(x = y = 10\) which also satisfies given inequality. \(x≥y\)
Answer for both is Option D.
The car does not stop and takes exactly 10 hours (Total time) to complete the journey of 100 miles (Total distatnce)
It is also known that x is greater than or equal to y. \(x≥y\)
Distance = Speed * time
Therefore, Distance traveled in first part of stretch of x mph = x*5 (5 is one half of total time 10Hrs)
Similarly, Distance traveled in later stretch of y mph = y*5
Total Distance = 100 miles
\(5x+5y = 100\)
Therefore,
\(x+y = 20\)
\(y=20 - x\)
and given \(x≥y\)
Therefore, now substituting y here.
\(x≥20-x\)
\(2x≥20\)
\(x≥10\)
now check for values from table, check for x=10,20,50
you will notice the only x=10 will satisfy based on given equation and will give you value of as y=10.
So both \(x = y = 10\) which also satisfies given inequality. \(x≥y\)
Answer for both is Option D.
19 Jul 2024, 13:30
Kudos
Bookmarks
The stem gives us this information:
X --> 1/2 time
y --> 1/2 time
Total trip was 10 hours and 100 miles
Dx = 5x
Dy = 5y
5x+5y = 100, and we can start solving backwards, till we get that x=y=10
Answer for both is 10
X --> 1/2 time
y --> 1/2 time
Total trip was 10 hours and 100 miles
Dx = 5x
Dy = 5y
5x+5y = 100, and we can start solving backwards, till we get that x=y=10
Answer for both is 10
19 Jul 2024, 13:42
Kudos
Bookmarks
Only x= 10 and y=10 satisfy the given conditions as total distance covered= 100 miles and also we know 5x+5y=100 where x is greater than or equal to y
Thus x=10 and y= 10 is our answer
Thus x=10 and y= 10 is our answer
