Two girls go on a road trip . They travel x + 5 km on the first day.They travel 2 km more than half of the distance they travel on the first day, on the second day.  On the third day they drove...

Two girls go on a road trip . They travel x + 5 km on the first day.

They travel 2 km more than half of the distance they travel on the first day, on the second day.  On the third day they drove three times as far as they did on the second day. If they drove 5000 km find the value of x.

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The distance  the two girls travel one the first day = x+5km.

The distance they travel on the second day = 2 km + (1/2) the distance travel on the 1st day = 2+(1/2)(x+5) km

The distance they travel on the 3rd day  = 3 times the distance they travel on the 2nd day  = 3 {2+(1/2)(x+5)}

The total length of the travel = (x+5)+ {2+(1/2)(x+5)} +3{2+(1/2)(x+5)} which is equal to 5000 kms. This gives us the equation:

x+5 + 2+ (1/2) (x+5) +6 +(3/2)(x+5) = 5000

x+13 + (1/2+3/2)(x+5) = 5000

x+13 +2(x+5) = 5000

x+ 13 +2x+10 = 5000

3x+23 = 5000

 3x= 5000-23 = 4977

x = 4977/3

 x = 1659.

Therefore the value of x = 1659 km.

william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

From the data with us:

The girls travel x+5 on the first day

On the second day they travel (x+5)/2 + 2

On the thirds day they travel [(x+5)/2 + 2]*3

In total they travelled 5000 km.

Therefore

x+5 + (x+5)/2 + 2 + [(x+5)/2 + 2]*3 = 5000

=> x+5 +x/2 + 5/2 +2 + 3x/2 + 15/2 + 6 = 5000

=> 2x + 10 +x +5 + 4 +3x +15 + 12 = 10000

=> 6x + 42 = 10000

=> x = (10000-42)/6

=> x = 1659.66

Therefore the value of x is 1659.66

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The distance they drove on the first day: (x+5) (1)

The distance they drove on the second day: 2 + (x+5)/2 (2)

The distance they drove on the third day: 3 [2 + (x+5)/2] (3)

The total distance they travelled:

(1)+(2)+(3) = 5000

We'll substitute (1),(2),(3).

(x+5) + 2 + (x+5)/2 + 3 [2 + (x+5)/2] = 5000

We'll remove the brackets:

(x + 5) + 2 + (x+5)/2 + 6 + 3(x+5)/2 = 5000

We'll combine like terms:

(x + 5) + 8 + 4(x+5)/2 = 5000

(x + 5) + 8 + 2(x + 5) = 5000

3(x+5) = 5000-8

3(x+5) = 4992

We'll divide by 3:

x + 5 = 1664

We'll subtract 5 both sides:

x = 1664 - 5

x = 1659 km

Verify:

The distance they drove on the first day:

(x+5)=1659 + 5 = 1664

The distance they drove on the second day:

2 + (x+5)/2 = 2+1664/2 = 2 + 832 = 834

The distance they drove on the third day: 3 [2 + (x+5)/2]

3 [2 + (x+5)/2] = 3*834 = 2502

1664 + 834 + 2502 = 5000 Km

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