It takes a plane 3.5 hours to fly 2345 miles and two hours to fly 860 miles going the opposite direction on the same route

Question

A how fast does the plane fly during the first leg of the trip

B how fast does the plane fly during the last leg of the trip

C what system of equations might be helpful in this scenario

D solve the system of equations using the best method

E how fast is the wind

F how fast does the plane fly without any  wind

Answer 1

P is the speed of the plane.

W is the speed of the wind. 

 

We really need to know when the plane was flying against the wind:

 on the 2345 mile flight or on the 860 mile flight?

 

If the distances were the same, we can tell by the times,

as the wind will slow down the plane.

But they are different, so we can't.

 

A typical plane flies around 500 mph.

2345/3.5 = 670 while 860/2 = 430.

So judging by these speeds, it appears as though

the plane was flying with the wind on the 2345 mile

flight.

 

Proceeding as such, using these calculations

of dividing by the times:

 

2345 = (P +w)*3.5 ---> 670 = P + w

860 = (P-w)*2   ------> 430 = P-w

 

Adding these equations together:

 1100 = 2P

 

P = 550

w=120

 

A) 550+120 = 670

B) 550-120 = 430

C) and D) done above

E) wind speed is 120

F) plane speed is 550