Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

math pre calc 11 question ?

Jim and Jon drove to Tofino to go surfing. Jim drove the first half of the trip at 110 km/hr and Jon drove the remaining half at 80 km/hr. If the trip took three hours and 30 minutes, how far is it to Tofino?

I know the answer is 324 km, but I am quite unsure as to how to properly get to that answer as the ways am I solving this problem do not equal that answer. Thank you!

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  • ?
    Lv 7
    2 months ago

     Jim and Jon drove to Tofino to go surfing. 

     Jim drove the first half of the trip at 110 km/hr and 

     Jon drove the remaining half at 80 km/hr. 

     If the trip took three hours and 30 minutes, 

     how far is it to Tofino?

     x/220 + x/160 = 7/2

     x ≈ 324.21 km

  • 2 months ago

    Let x km be the distance from their starting place to Tofino. Then

    x/[2(110)]+x/[2(80)]=3.5

    =>

    (8x+11x)/880=7

    =>

    x=324.21~324 km

    (rounding up to 1 km)

  • 2 months ago

    half of the trip = time or distance

    is the tricky part.

  • Ian H
    Lv 7
    2 months ago

    Let half of the total distance be d.

    d/110 + d/80 = 19d/880 = 7/2 hours

    2d = (2*7*440)/19 = 6160/19 ~ 324.2 km

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  • Let the distance be 2x

    110 km/hour * t[1] hour = x km

    80 km/hour * t[2] hour = x km

    t[1] + t[2] = 3.5 hours

    110 * t[1] = x

    80 * t[2] = x

    Therefore

    110 * t[1] = 80 * t[2]

    11 * t[1] = 8 * t[2]

    1.375 * t[1] = t[2]

    t[1] + t[2] = 3.5

    t[1] + 1.375 * t[1] = 3.5

    2.375 * t[1] = 3.5

    t[1] = 3.5 / 2.375

    t[1] = 7 / 4.75

    t[1] = 14 / 9.5

    t[1] = 28/19

    110 * t[1] = x

    110 * (28/19) = x

    110 * (19/19 + 9/19) = x

    110 + 110 * 9/19 = x

    110 + (95 + 15) * 9 / 19 = x

    110 + 95 * 9/19 + 15 * 9/19 = x

    110 + 5 * 9 + 135/19 = x

    110 + 45 + 133/19 + 2/19 = x

    155 + 7 + 2/19 = x

    162 + 2/19 = x

    Total distance is 2x

    2 * (162 + 2/19) =>

    324 + 4/19

    To 3 sf

    324 km

  • ?
    Lv 7
    2 months ago

    Let the time be 't'

    110km/hr (1/2t) + 80km/hr (1/2 t) = d

    We know that t=3.5 hr, so 1/2t = 1.75

    Sub in, and solve for d = 332.5 km

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