On a bushwalk, Abby covers 1/2 of the distance on the first day. The track was more difficult on the second day so she only covered 1/3 of the total distance. She walked a total of 35 km in the two...

On a bushwalk, Abby covers 1/2 of the distance on the first day. The track was more difficult on the second day so she only covered 1/3 of the total distance. She walked a total of 35 km in the two days. Find the distance Abby has to cover to complete the walk. 

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gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

Distance covered by Abby =  1/2 + 1/3 of the total distance = 5/6 of total distance

Total distance walked in 2 days = 35 km 

thus 5/6 of distance = 35 km

or total distance that was to be covered = 35 *6/5 = 42 km

i.e. Abby still has to walk (42-35) = 7 km.

violy's profile pic

violy | High School Teacher | (Level 1) Associate Educator

Posted on

Let set `x` be the total distance that Abby needed to complete.
So, we can represent the distance that she traveled on the first day as `1/2x` .
We can write the distance that she traveled on the second day as `1/3x` .
We know that the total distance that she was able to travel for two days is` 35` km ,
total is the answer when we are adding, so we will add `1/2x` and `1/3x` .
`1/2x + 1/3x = 35 `

We need to solve for `x` first, before we can find the distance that Abby needed to travel in
order to complete the walk.

`1/2x + 1/3x = 35 `

Find the LCD (least common denominator).
Finding the LCD is like finding the LCM (least common multiple).

So, we need to list the multiples of `2 ` and `3` .
Multiples of `2` :` 2, 4, 6, 8, 10, 12, 14, 16, 18, 20` .
Multiples of `3` : `3, 6, 9, 12, 15, 18, 21, 24, 27, 30` .

The least common multiple is `6` , so the LCD is `6` .
Multiply both sides by `6` .

`1/2x + 1/3x = 35 `


`(6*1x)/2 + (6*1x)/3 = 6*35`

`3x + 2x = 210`

Combine like terms.
`5x = 210`

Isolate the `5` on left side, by dividing both sides by `5` .
`(5x)/5 = 210/5`
`x = 42`

Therefore, the total distance is` 42` km.
To find the remaining distance, we will apply subtraction.
`42` km `- 35` km `= 7` km

Hence, Abby needs to travel `7` km to complete the walk .

That is it!

electreto05's profile pic

electreto05 | College Teacher | (Level 1) Assistant Educator

Posted on

Should be considered, the following equation:

(1/2)x + (1/3)x = 35

Where the variable x represents our incognita.

Isolating x we have:

1/3 + 1/2 = 5/6

(5/6)x = 35

x = (6)(35)/5

x = 42 km

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