# distance questionTwo 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...

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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On the first day the girls traveled x + 5 km

On the second day they travel 2 more than half the distance they traveled on the first day. That is equal to (x + 5)/2 + 2

On the third day they traveled 3 times as far as they did on the second. That is equal to 3[(x + 5)/2 + 2]

The total distance traveled is 5000. That is equal to x + 5 + (x + 5)/2 + 2 + 3[(x + 5)/2 + 2]

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

=> 3x + 23 = 5000

=> x = (5000 - 23)/3

=> x = 1659

**The value of x = 1659**

You should come up with the following substitution:

x + 5 = y

The girls covered 5000 km along the three days of the trip.

Each day, they cover a number of km such that:

- first day: y km

- second day: 2+y/2

- third day: 3*(2+y/2) = 6 + 3y/2

The number of km covered is the result of the sum of the kms covered each day such that:

5000 = y + 2 + y/2 + 6 + 3y/2 => 5000 = y + 8 + 4y/2 => 3y = 5000-8

3y = 4992 => y = 1664 => x + 5 = 1664 => x = 1664 - 5 => **x = 1659 Km**

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