Question on speed with no wind

Question

Dylan flies a plane against a headwind for 2400 miles. The return trip with the wind took 20 hours less time. If the wind speed is 10 mph, how fast does Dylan fly the plane when there is no wind?

Answer 1

Let V be Dylan's  plane velocity.

 

10mph the Head wind

 

The rate equation is rate X time = distance

 

V- 10 is Dylan's ground velocity on the first trip.

 

V + 10 is Dylan's ground velocity on the return trip.

 

t1 is travel time on first trip

 

t1- 20 is travel time on return trip

 

So  (V - 10)t1 = 2400  and (V + 10)(t1 -20) = 2400

 

All we have to do is solve for t1 in the first equation and plug it in the second equation and solve for V

 

t1 = 2400/(V- 10)

 

now plug t1 in the second equation

 

(V + 10)((2400/(V-10)) - 20) = 2400

 

now solve for V

 

2400 ((V+ 10)/(V- 10)) - 20(V+10) = 2400

 

multiply both sides of the equation by V-10:

 

2400(V+10) - 20(V² - 100) = 2400(V-10)

 

subtracting 2400V from both sides and multiplying through the parenthesis.

 

24000 - 20V² - 2000 = -24000

 

subtracting 24000 from both sides

 

-20V² - 2000 = -48000

 

adding 2000 to both sides

 

-20V² = -46000

 

dividing both sides by -20

 

 V² = 2300

 

taking the square root of both sides

 

V =47.96 mph