Question

There were 3 parts to Ritas race she ran the first part which was 4/9 of the total distance, in 20 minutes she ran the second part which was 2/5 of the remaining distance, in 12 minutes. She finally ran the third part in 15 minutes at the speed of 300 meters per minute.

How long was the first part of the race? What was Ritas speed in that section of the race?

Answer 1

3/5 .................................. 6/9

Step-by-s4tep explanation:

Answer 2

300 meters per minute

Explanation:

Step 1

Determine the fraction of the total distance for each part of the race.

Given:

• 1st part of race = 4/9 of total distance

• 2nd part of race = 2/5 of remaining distance

`\begin{aligned} \implies \sf 2nd\:part & = \sf (2)/(5)\:of\:remaining\:distance\\ & = \sf (2)/(5) *\left(1-(4)/(9)\right)\\& = \sf (2)/(9)\:of\:total\:distance\end{aligned}`

`\begin{aligned}\implies \sf 3rd\:part & = \sf 1-1st\:part-2nd\:part\\& = \sf 1-(4)/(9)-(2)/(9)\\& = \sf (1)/(3)\:of\:total\:distance\end{aligned}`

Step 2

Determine the distance of the third part of the race.

Given:

• time = 15 minutes
• speed = 300 meters per minute

`\begin{aligned}\sf Distance & = \sf speed * time\\& = \sf 300 * 15\\& = \sf 4500 \:\:meters\end{aligned}`

Step 3

If the third part of the race (which is 1/3 of the total distance) is 4500m, then the distance of the whole race is:

`\begin{aligned} \sf Total\:distance & = \sf 4500 * 3\\& = \sf 13500\:meters \end{aligned}`

Step 4

Determine the distance of the 1st part of the race:

`\begin{aligned}\sf Distance\:of\:1st\:part\:of\:race & = \sf (4)/(9) \:of\:total\:distance\\& = \sf (4)/(9) * 13500\\& = \sf 6000\:meters \end{aligned}`

Step 5

Determine the speed of the 1st part of the race:

Given:

• time = 20 minutes
• distance = 6000 m

`\begin{aligned}\sf Speed\:of\:1st\:part\:of\:race & = \sf (distance)/(time)\\& = \sf (6000)/(20)\\ & = \sf 300\:meters\:per\:minute\end{aligned}`