SOLUTION: A plane traveled from Moncton to Winnipeg, a distance of 1940km. On the return trip, the plane’s speed increased by 100km/h due to a tailwind. The total round trip took 6 hour

Question 1195809: A plane traveled from Moncton to Winnipeg, a distance of 1940km. On the return
trip, the plane’s speed increased by 100km/h due to a tailwind. The total round trip took
6 hours. Find the average speed of the plane in both parts of its journey.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A plane traveled from Moncton to Winnipeg, a distance of 1940km. On the return
trip, the plane’s speed increased by 100km/h due to a tailwind. The total round trip took
6 hours. Find the average speed of the plane in both parts of its journey.
--------------
v = plane's groundspeed with no wind.
----
Avg speed of the round-trip = 2*v*(v+100)/(v + v+100) = (2v^2 + 200v)/(2v+100)
Avg speed = 1940*2/6 = 1940/3 km/hr
---
(2v^2 + 200v)/(2v+100) = 1940/3
(6v^2 + 600v)/(2v+100) = 1940
6v^2 + 600v = 1940*(2v+100)
3v^2 + 300v = 970*(2v+100) = 1940v + 97000
3v^2 - 1640v - 97000 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=3853600 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 600.509806271784, -53.8431396051169. Here's your graph:

Ignore the negaive value
v = 600.5 km/hr

RELATED QUESTIONS
Every hour on the hour, beginning at midnight, a mail truck leaves Winnipeg for Regina,... (answered by ikleyn)

A Jet flew from Montreal to San-Francisco, a distance of 4000 km. On the return trip the (answered by drk)

A plane travels from city A to city B, a distance of 1500 miles, in 6 hours. On the... (answered by ewatrrr)

a plane travels from city a to city b, a distance of 1500 miles, in 6 hrs. On the return... (answered by ewatrrr)

Every hour on the hour, beginning at midnight ,a mail truck leaves Winnipeg for Regina... (answered by ikleyn)

A bus covered the 400-km distance between points A and B at a certain speed. On the way... (answered by Boreal)

one weekend members of a cycling club rode on the KVR trail uphill from penticton on... (answered by ikleyn)

A jet traveled to Calgary, Alberta from St. John’s , Newfoundland, a distance of 4200... (answered by josgarithmetic)