Answer the following questions concerning a two-way flight from Miami to Dublin.

Question

A plane made a two-way flight from Miami to Dublin. The trip from Miami to Dublin took four more hours than the return trip from Dublin to Miami. The cause for the difference in flight times were winds over the ocean, which averaged 50 km/hr on the return trip. Assume there was no wind on the trip to Dublin. The total distance travelled both ways was 9900 km. Let x represent the average speed of the plane in still air (no wind).

a) Represent time going from Dublin to Miami as a rational expression.

b) Represent the time going from Miami to Dublin as a rational expression.

c) Write an equation representing the relationships between the times.

d) What was the average rate of the plane in still air.

e) How long did the round trip take?

*NOTE*

Grade 12 Advanced Functions (MHF4U)

Please answer clearly and neatly.

Thanks

Answer 1

Distance = time × rate

a) The rate from Dublin to Miami was assisted by the wind or x+50.

t₁ = 9900/(x+50)

b) Miami to Dublin: t₂ = 9900/x

c) t₂ = t₁ + 4

d) 9900/x = 9900/(x+50) + 4

9900/x = (9900 +4x + 200)/(x+50)

9900(x+50) = x(9900+4x+200)

9900x + 50(9900) = 9900x +4x²+200x

4x²+200x-50(9900) = 0

x²+50x-25(4950) = 0

x = 337.66, -377.668 Ignore the negative result

x = 337.66 km/hour

e) t₁ = 9900/(387.66) = 25.54 hours

t₂ = 29.54 hours

Total time = 55.08 hours

Answer 2

start with the distance formula. distance = rate * time Because part a and part b are asking for expressions of time, then we will use time = distance/rate

Part a) Dublin to Miami. What we know; this took less time than Miami to Dublin there was wind that averaged 50KM/hr, the distance is half of 9,990KM or 4,995KM

I think it would be easier to start with Part b) Miami to Dublin. First of all, no wind so the rate is just "x" as defined in the problem. time from M to D = 4,995/x

Now, go back to part a) time from D to M is the same distance 4,995KM, but how does the rate change? The wind averages 50KM/hr. Did the wind slow down the plane, a negative impact or speed up the plane, a positive impact?

Let me know if you need more help.