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Maths Week: Your Saturday puzzle

The remix to addition.

IT’S MATHS WEEK, and as is our annual tradition here, we’re setting you a puzzle a day this week with all answers published on the site tomorrow.

Get puzzling!

TODAY’S Q: 

Two friends meet up to run around a 5km circuit.

Ann runs at 12 km/h and Bill runs at 8 km/h.

They start together but decided to run in opposite directions.

How far will Ann have run when they pass each other?

The following day they meet again and decide to run in the same direction but each would run at their own pace.

How far would Ann have to run to lap Bill?

All answers will be published on TheJournal.ie tomorrow. 

On a roll? Try some more of our Maths Week puzzles here.

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11 Comments
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    Install the app to use these features.
    Mute Marc Bryan
    Favourite Marc Bryan
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    Oct 20th 2018, 5:34 PM

    What? A woman can run faster than a man? Surely that’s not right!

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    Mute mick scanlan
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    Oct 20th 2018, 5:38 PM

    @Marc Bryan: surely can when the bill arrives

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    Mute Marc Bryan
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    Oct 20th 2018, 5:43 PM

    @mick scanlan: Lol!!!

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    Mute Johnny B Goode
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    Oct 20th 2018, 10:39 PM

    @Marc Bryan: Have you not seen the state of Bill lately anyway?

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    Mute Mark Carlow
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    Oct 20th 2018, 6:01 PM

    1. 3km
    2. 15km

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    Mute Mr. Dragmire
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    Oct 20th 2018, 8:42 PM

    (i) (12/8)x + x = 5, therefore x = 2 which is how far Bill went. 5-2= 3km

    (ii) relative velocity is 12-8=4 so the time to overtake would be the same as if Bill waited at the start line and Ann ran at 4km/hr. Her time to run 5k at 4km/hr is 5/4 or 1.25hrs.

    1.25hrs x her actual velocity of 12 = 15km

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    Mute Eoin Faz
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    Oct 20th 2018, 5:53 PM

    3km

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    Mute Seany Leary
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    Oct 20th 2018, 7:46 PM

    3.333ish

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    Mute David Byrne
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    Oct 21st 2018, 2:22 AM

    Black and gold

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    Mute Barry Sutton
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    Oct 21st 2018, 9:40 AM

    Ratio of Ann’s speed to Bills is 12/20 km/h to 8/20 km/hr

    = 3/5 to 2/5
    i) 3/5 of lap distance is 3/5 x 5km
    = 3km

    ii) Point Ann overlaps Bill =
    (Ratio of Bills speed to Ann’s)x(Total distance) = (Ratio of Ann’s speed to Bills)x(total distance) less the ratio of Ann’s speed to Bills by the circuit length(5km)

    (2/5)x = (3/5)(x-5)
    0.4x = 0.6x – 3
    0.6x-0.4x = 3
    x = 3/0.2
    x = 15Km

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    Mute BatMon
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    Oct 20th 2018, 7:47 PM

    1 = 3 klm
    2 = 5 klm

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