P6 Speed Problem

• kkhing

  31 Mar 09, 22:56

  Can someone help me with this question? Thanks.

  Two brothers, Harry and Potter always cycle from home to school at the same time. Harry's average speed is 7km/h while Potter's speed is 5.6km/h. One day, after cycling for 12 minutes, Harry realised that he had forgotten to bring his bag along. He cycled back home immediately to get his bag while Potter continued his journey to school. Without changing his usual speed, Harry reached school at the same time as Potter. Find the distance between their home and school.

• Rednano

  31 Mar 09, 23:00

  go draw a bar diagram...
  
  distance at stop point from harry home: 7km / 5 = 1.4km

• wee_ws

  1 Apr 09, 05:39

  Hi,

    We note that ratio of Harry's average speed : Potter's average speed is 5 : 4. So Harry covers 5 parts of distance while Potter covers 4 parts of distance in the same period.

    After 12 minutes:
    Distance of Harry from Home = 7 / 5 = 1.4 km
    Distance of Potter from Home = 5.6 / 5 = 1.12 km

    After 24 minutes:
    Distance of Harry from Home = 0 km
    Distance of Potter from Home = 2.24 km

    After 36 minutes:
    Distance of Harry from Home = 1.4 km
    Distance of Potter from Home = 3.36 km

    At this point (36th minute), Harry has to cover 5 parts for the remaining distance and Potter has to cover 4 parts for the remaining distance in order for both to reach school at the same time.

    Thus, taking the difference, we obtain: 
    one part -> 3.36 - 1.4 km, i.e. one part -> 1.96 km.

    Distance of school from home = ? x 1.96 + ? km

    Thanks!

  Cheers,
  Wen Shih

• wee_ws

  1 Apr 09, 05:45

  Hi,

    The method via algebra is much easier.

    Let x represent distance between the point where Harry stopped and the school.

    Then (x + 4.2)/7 = (x + 1.4)/5.6.

    Thanks!

  Cheers,
  Wen Shih

• baiyun

  1 Apr 09, 10:12

  Hi,hope this helps.

  

• FirePig

  1 Apr 09, 11:08

  harry: potter

  Speed = 7:5.6

  Time 5.6u:7u

  1.4u = 24mins

  14u = 240 mins

  7u = 120 mins

  Total distance = 5.6 km/h x 2 hours =  11.2km

   

• MaNyZeR

  1 Apr 09, 13:34

  Yeah 11.2km.. is the correct answer