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primary 6 | Maths

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If you checked your answers ,

Time taken for Eric to cycle to school

= 60km ÷ 10km/h

= 6h

Time taken for Eric's uncle to drive him back home

= 60km ÷ 30km/h

= 2h

That's a difference of 4 hours.

If he takes ⅓ hour less to get home, it also means he takes ⅓ hour more to get to school.

What If :

his uncle didn't stop when he reached home, then in the same amount of time that he uses to get to school, his uncle would have driven for another extra ⅓ hour than originally.

⅓ h × 30km/h = 10km

This means that in the same amount of time taken to get to school, the distance travelled by driving would be 10km more than the distance from school to home (by cycling)

30km/h - 10km/h = 20km/h

For every hour, distance travelled by driving is 20km more than by cycling.

Since he would have travelled 10km more by driving than cycling as seen above,

10km ÷ 20km/h = ½h

This means that the time taken to get to school by cycling is ½h.

Distance between school and home

= ½h × 10km/h

= 5km

① Since he took ⅓ hour more to get to school from home,

In the same amount time he used to get home, he would not have reached school yet and would still have another ⅓ hour to cycle.

Distance left to cycle in ⅓ hour

= ⅓h × 10km/h

= 3⅓ km

This tells us that he had 3⅓km left to cycle. And this implies that in the same amount of time used to drive home, the distance travelled by driving is 3⅓ km more than by cycling.

30km/h - 10km/h = 20km/h

Every hour, driving covers 20km more than cycling.

Since only 3⅓ km more is covered,

3⅓ km ÷ 20km/h

= 10/3 km × 1/20 km/h

= 1/6 h

This tells us that the time taken to drive home is 1/6 h only.

Distance between home and school

= 1/6 h × 30km/h

= 5km

Let x km be the distance between school and home.

Time taken to travel to school by cycling

= x km ÷ 10 km/h

= x/10 h

Time taken to travel home by driving

= x km ÷ 30 km/h

= x/30 h

Since driving uses ⅓ hour less time,

x/10 h - x/30 h = ⅓ h

x/10 - x/30 h = ⅓

Multiply both sides by 30,

3x - x h = 10

2x = 10

x = 10 ÷ 2

x = 5

So distance between school and home is 5 km

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