Question

Question #febe7

Answer 1

Bill has to run `2 7/8` laps on Friday to reach his target.

Explanation:

First we calculate the distance Bill has run on each day of the week from Monday to Thursday. We do that by converting the mixed fractions into improper fractions (by multiplying the whole number by the denominator and adding the product to the numerator) and multiplying them by `400`, the distance of each lap in metres.

Monday:

Number of laps: `1 1/4=5/4`

Distance: `5/4xx400=5/(1cancel4)xx100cancel400=5xx100=500m`

Tuesday:

Number of laps: `1 3/4=7/4`

Distance: `7/4xx400=7/(1cancel4)xx100cancel400=7xx100=700m`

Wednesday:

Number of laps: `1 5/8=13/8`

Distance: `13/8xx400=13/(1cancel8)xx50cancel400=13xx50=650m`

Thursday:

Number of laps: `2 1/2=5/2`

Distance: `5/2xx400=5/(1cancel4)xx200cancel400=5xx200=1000m`

Now we add the four distances to determine the total distance run by Bill in four days.

The total distance is `(500+700+650+1000)=2850m`

Bill wants to run a total of `4000m` in five days, so he would have to run `(4000-2850)=1150m` on Friday to achieve that total.

Since `1` lap is `400m`, we divide that distance by `400` to calculate how many laps Bill has to run.

`1150/400=(115cancel0)/(40cancel0)=(23cancel115)/(8cancel40)=2 7/8`

Bill has to run `2 7/8` laps on Friday to reach his target.

Answer 2

`2 frac(7)(8)` laps

Explanation:

First, let's add up the total number of laps up to, and including, Thursday:

`Rightarrow "Total number of laps" = 1 + frac(1)(4) + 1 + frac(3)(4) + 1 + frac(5)(8) + 2 + color(red)(1/2)`

`color(red)(1/2)xx4/4=color(red)(4/8)`

`Rightarrow "Total number of laps" = 5 + frac(4)(4) + frac(5)(8)+ frac(4)(8)`

`Rightarrow "Total number of laps" = 5 + 1 + frac(9)(8)`

`Rightarrow "Total number of laps" = 6 + 1 + frac(1)(8)`

`therefore "Total number of laps" = 7 frac(1)(8)`

Now, each lap is `400` `"m"` long.

So by the end of Thursday, Bill has run `7 frac(1)(8) times 400 = 2850` `"m"`.

However, Bill wants to run a total of `4000` `"m"`.

Let's calculate how much more he must run to reach `4000` `"m"`:

`Rightarrow "Remaining distance to run" = 4000` `"m"` `- 2850` `"m"`

`therefore "Remaining distance to run" = 1150` `"m"`

Finally, let's convert this distance back into a number of laps:

`Rightarrow "Number of laps" = frac(1150)(400)` `"laps"`

`Rightarrow "Number of laps" = frac(23)(8)` `"laps"`

`Rightarrow "Number of laps" = frac(16)(8) + frac(7)(8)` `"laps"`

`therefore "Number of laps" = 2 frac(7)(8)` `"laps"`

Therefore, Bill must run `2 frac(7)(8)` laps on Friday.