Question

A jet can travel 4550 km in 5 hours with the wind. The return trip against the wind takes 6.5 hours. Find the rate of the jet with no wind. You will earn points for writing the correct system of equations for this word problem and points for solving it correctly and answering the question in a complete sentence

Answer 1

I think

Let the speed of the plane be v and the speed of the wind w.
Then v+w = 4550/5=910
and v-w = 4550/6.5=700
So v=(910+700)/2=805.
The rate of the jet with no wind is 805 km/h.??

Answer 2

'With no wind' I presume means with no wind in it's favour [ie against it]

So taking this into account, we know it travels 4550km in 6.5 hours
The rate of the jet I would take to be the speed

Speed = distance / time

Working in unit speed, you would need to convert time to seconds, and distance to metres.
This will give you the rate [speed] in standard units.

In response to what you wrote above, the speed of the wind is not defined, it merely says that the plane travels the distance in 5 hours, not the specifying the speed or impact of the wind, so this has no place in the equation.

Hope this helps!

Answer 3

Well, let's check it out. If the plane goes 805 km/h and the speed with the wind is 910 km/h, that means the wind speed is 910-805 = 105 km/h

Flying with the wind (tail wind): 5 hr * (805 km/h + 105 km/h) = 4550 km
Flying against the wind (head wind): 6.5 hr * (805 km/h - 105 km/h) = 4550 km

Solution checks.

Answer 4

@sarahusher that's a good example of setting up the work for one of these problems, have a look!

Answer 5

Thanks :D a lot @whpalmer4 and @sarahusher