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

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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) About Me  (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.
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v = plane's groundspeed with no wind.
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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 ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-1640x%2B-97000+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1640%29%5E2-4%2A3%2A-97000=3853600.

Discriminant d=3853600 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1640%2B-sqrt%28+3853600+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1640%29%2Bsqrt%28+3853600+%29%29%2F2%5C3+=+600.509806271784
x%5B2%5D+=+%28-%28-1640%29-sqrt%28+3853600+%29%29%2F2%5C3+=+-53.8431396051169

Quadratic expression 3x%5E2%2B-1640x%2B-97000 can be factored:
3x%5E2%2B-1640x%2B-97000+=+%28x-600.509806271784%29%2A%28x--53.8431396051169%29
Again, the answer is: 600.509806271784, -53.8431396051169. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-1640%2Ax%2B-97000+%29

Ignore the negaive value
v = 600.5 km/hr