what is The distance from Fairbanks to Coldfoot is enter your response here mi.

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Part 1

Alex hauled a load of pipe from Fairbanks to Deadhorse on a highway in a record time of

23 hours 15 minutes. From Fairbanks to Coldfoot he averaged 30 mph. Because of a​ blizzard, he averaged 10 mph less from Coldfoot to Deadhorse. If Coldfoot is the halfway​ point, then what is the distance from Fairbanks to​ Coldfoot?

Answer 1

It helps to draw a diagram to visualize the problem. From the words, there are two legs of the trip. Leg 1 he travels from Fairbanks to Coldfoot at 30mph. Leg 2 he travels from Coldfoot to Deadhorse at 20 mph (10 mph less than the first leg).

You can use the distance equation of D = V*t (D is distance, V is velocity, and t is time) to create equations to represent the trip across each of the legs.

For leg 1, D₁ = 30t₁

For leg 2, D₂ = 20t₂.

Since Coldfront is half the distance between the two locations, we also know:

D1 = D2

So we can replace D1 and D2 with a singular D variable representing the distance for both.

D = 30t₁ (equation 1)

D = 20t₂.(equation 2)

The whole trip took 23 hours and 15 minutes (or 23.25 hours, since we need the units to align with the velocity - mph or miles per hour) which we can represent with the equation:

t₁ + t₂ = 23.25 (equation 3)

Now we have three equations with three unknowns, so we can solve. Let's first equate the two D equations to get:

D₁ = D₂

30t₁ = 20t₂

(divide both sides by 30)

t₁ = 2/3t₂

Now we can plug this t₁ value into equation 3.

t₁ + t₂ = 23.25

2/3t₂ + t₂ = 23.25

(add the variables)

5/3t₂ = 23.25

(multiple both sides by 3/5 to cancel the fraction by the t₂)

t₂ = 13.95 hours

Now we can solve for t₁ using equation 3.

t₁ + t₂ = 23.25

t₁ + 13.95 = 23.25

(subtract 13.95)

t₁ = 9.3 hours

Now we can plug this into equation 1 to get the distance from Fairbanks to Coldfoot.

D = 30t₁

D = 30(9.3)

D = 279 miles

Answer 2

F to C 30 mph

C to D 30-10= 20 mph

F to D 23 1/4 hours

F to C =30(x) miles

=C to D = 20(23.25-x) miles

30x= 20(23.25)-20x

30x+20x= 465

x=465/50= 9.3 hours from F to C

23.25-9.3= 13.95 hours from C to D

30(9.3)+20(13.95)

=279+279

= 558 miles from Fairbanks to Deadhorse