Let's denote the rate of the jet in still air as 'j' (in miles per hour) and the rate of the wind as 'w' (in miles per hour).

From the problem, we have two equations based on the given information:

1) When the jet travels against the wind, the rates subtract, so we have: j - w = 3170 miles / 5 hours = 634 mph.

2) When the jet travels with the wind, the rates add, so we have: j + w = 4170 miles / 5 hours = 834 mph.

Now we have a system of two equations:

j - w = 634
j + w = 834

We can solve this system of equations by adding the two equations together:

2j = 1468

Dividing both sides by 2 gives the rate of the jet in still air:

j = 1468 / 2 = 734 mph.

Substituting j = 734 into the first equation gives:

734 - w = 634
w = 734 - 634 = 100 mph.

So, the rate of the jet in still air is 734 mph and the rate of the wind is 100 mph.

Question

Let's denote the rate of the jet in still air as 'j' (in miles per hour) and the rate of the wind as 'w' (in miles per hour).

From the problem, we have two equations based on the given information:

1) When the jet travels against the wind, the rates subtract, so we have: j - w = 3170 miles / 5 hours = 634 mph.

2) When the jet travels with the wind, the rates add, so we have: j + w = 4170 miles / 5 hours = 834 mph.

Now we have a system of two equations:

j - w = 634
j + w = 834

We can solve this system of equations by adding the two equations together:

2j = 1468

Dividing both sides by 2 gives the rate of the jet in still air:

j = 1468 / 2 = 734 mph.

Substituting j = 734 into the first equation gives:

734 - w = 634
w = 734 - 634 = 100 mph.

So, the rate of the jet in still air is 734 mph and the rate of the wind is 100 mph.

Knowee AI · Accepted Answer