Question

passenger plane flew from Texas to Frankfurt and back: The round trip is 9900 km. The return trip took hours less than the trip to Frankfurt because of the 50 km/hr wind over the ocean on the return trip. Assume there Was no wind On the trip to Frankfurt. Let x km/h represent the average speed of the plane in still air:
a). Express the trip time from Texas to Frankfurt as a rational function of variable
b) . Express the trip time from Frankfurt to Texas as a rational function of variable x
c) Write an equation representing the relationships between the two trip times
d)Find the average speed of the plane in still air [3marksl e). How long did the round trip take?

Answer 1

speed of plane in still air --- x km/h <--- speed for T to F
speed of plane on F to T trip ---- x + 50 km/h

time taken to go from Texas to Frankfurt = 4950/x hours
time taken to go from Frankfurt to Texas = 4950/(x+50)

"The return trip took hours less than the trip to Frankfurt"
<b>------ missing the number of hours, let's assume the difference was 3 hours, then the equation would be </b>

4950/x - 4950/(x+50) = 3

multiply each term by x(x-50)
4950x- 4950(x-50) = 3x(x-2)

Once you replace 3 with the correct difference in time, solve for x
using the quadratic formula. Make sure to use only the positive answer
since x is the speed of the plane.

sub in your x into the two "times" expressions above, then add them up
for a total time