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Sunday, November 18, 2007

Rosyth School 2006 PSLE Math Prelim Question

Mr and Mrs Wong left their house in the same car for Town P. Mr Wong drove at a speed of 60 km/h. Realizing that he left his lap-top at the home, he let Mrs Wong alight at a bus-stop and drove back to his house. Mrs Wong walked from the bus-stop at a speed of 4 km/h to Town P. It took her 45 min to reach Town P. Both Mr Wong and Mrs Wong arrived at Town P at the same time. Find the distance between their house and Town P.


Solution
(click on image below for clearer view)


Distance (bus-stop to Town P) ---- Speed x time
= 4km/h (Mrs Wong's walking spd) x 3/4h
= 3 km (distance from bus-stop to Town P)


Time for car to travel 3 km at 60 km/h (time = distance/speed)
= (3km) divided by (60 km/h)
= 3 min

Therefore it took Mr Wong 3 min to drive from bus-stop to Town P.

Since Mrs Wong took 45 min to walk from bus-stop to Town P, it also means that Mr Wong took 45 min to travel from bus-stop to their home, and from their home to Town P.

This means that the time Mr Wong took to travel from bus-stop to his home, and from his home to bus-stop again would be -

45 min – 3 min = 42 min


Distance covered by Mr Wong during that 42 min period -

Dist = speed x time

= 60km/h x 42min

= 60km/h x (42/60)h

= 42 km

42 km is the distance from bus-stop to home, then back to bus-stop again.

But distance from home to bus stop is only half of that, which is

1/2 x 42km

= 21 km (distance from home to bus-stop)


Distance from home to Town P therefore is

21 km (distance from home to bus-stop) + 3 km (distance from bus-stop to Town P)

= 24 km

Answer: The distance between their home and Town P is 24 km.
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3 comments:

  1. Anonymous2 September 2008 at 2:37 pm

    I would like to ask whether there are any way to help me understand speed questions better as those are the places I lose quite a lot of marks in.

    ReplyDelete
  2. Excel Eduservice3 September 2008 at 11:04 am

    Using diagrams like time lines, distance lines or speed lines help a lot.

    ReplyDelete
  3. Anonymous5 September 2008 at 4:16 pm

    1) Just remember 1 formula: Distance = Speed x Time

    2) Draw diagram and write down all information given.

    3) Based on the questions, what info do you need to find the answers.

    4) Check if info given (against formula) allow you to find the unknowns you want.

    5) The more difficult Speed problems normally involve different time, different speeds.
    Remove those (by finding / equating numbers to them) first if you could, so that you have the same starting and ending time, same speed, etc. and the problems would be easier to handle.

    Key: Keep in mind that the Difference in distance is due to the difference in speed over a certain time lapsed (and not the difference in time).

    ReplyDelete