I need help with part (iii) from the following question. I don't know how to solve for x. For part (i) i got t=20x/3 For part (ii) i got 11.5-x. 

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llltkl | College Teacher | (Level 3) Valedictorian

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Ethan cycles from home for x km at 9 km/h, to the MRT station. He waited for 3 minutes before cathing up the next MRT train. The MRT train travels at an average 60 km/h. He walks for ½ km at an average 6 km/h before reaching his school. The distance from home to his school by the above route is 12 km and the total time he spent is 28 minutes.

1. Distance travelled by cycle: =x km

2. He waits for 3 min.

3. Travels a distance by MRT train at 60 km/h

4. Walks 0.5 km to reach his school.

Total distance travelled is 12 km.

Therefore, distance traveled by MRT train=12-(x+0.5)=(11.5-x) km

1. Time required for his travel by cycle: =distance/average speed

`=x/9 h =x/9*60 min. =20x/3 min.`

2. He waits for 3 min.

3. Travels a (11.5-x) MRT train at 60 km/h, it takes `(11.5-x)*60/60 = (11.5-x) min.`

4. Walks 1/2 km at 6 km/h. Time required for his walk`=(1/2)/6*60 min. = 5 min.`

The total time required to reach his school from home is 28 min.

Therefore,

`20x/3+3+(11.5-x)+5=28`

`rArr 20x/3+8+(11.5-x)=28`

`rArr (20x+24+34.5-3x)/3=28`

`rArr(17x+58.5)=3*28=84`

`rArr 17x=84-58.5=25.5`

`rArr x=25.5/17=1.5`

So, Ethan travelled 1.5 km by cycling.

So, your first answer is correct. The expression for (ii) is also correct. Put the value of x in it and obtain the solution to (ii) as 10 km.

Sources:

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