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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•  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

• 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)

• half of the trip = time or distance

is the tricky part.

• 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

• Let the distance be 2x

110 km/hour * t hour = x km

80 km/hour * t hour = x km

t + t = 3.5 hours

110 * t = x

80 * t = x

Therefore

110 * t = 80 * t

11 * t = 8 * t

1.375 * t = t

t + t = 3.5

t + 1.375 * t = 3.5

2.375 * t = 3.5

t = 3.5 / 2.375

t = 7 / 4.75

t = 14 / 9.5

t = 28/19

110 * t = 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

• 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