Trying to find speed

Question

Hazel and Emilie fly from city A to city B. The flight from A to B is against the wind and takes 4 hr: The return flight with the wind takes 3.5 hr. If the wind speed is 28 mph, find the speed of the plane in still air

Answer 1

distance = velocity * time (D - V*T)

For this problem, V is the combination of the airspeed (V_a) and the wind speed.

The distance is the same in both cases, so we can just write V*T = V*T

Outbound, V = V_a - 28, T = 4

Return, V = V_a + 28, T = 3.5

So:

4(V_a - 28) = 3.5(V_a + 28)

4V_a - 3.5V_a = 28*7.5

0.5 V_a = 28*7.5

V_a = 28*15 = 420

CHECK

420 - 28 = 392

420 + 28 = 448

392 * (4/3.5) = 448

Answer 2

Hi Tulani!

This is a classic question where you need to understand the relationship between speed, distance and time (distance = speed*time or d = v*t). If you're new to this, here's an example:

1. EX: if you travel at a speed of 50mph for 3 hours, what distance do you travel?
2. We need to find d, and we're given v=50 mi/hr, t=3 hr
3. Using d=v*t, we have d=50 mi/hr *3 hr -> d=150 mi

The real trick to this question is recognizing that the plane is moving against the wind when traveling from A to B (total speed = plane speed - wind speed) and flying with the wind when flying from B to A (total speed = plane speed + wind speed). If we call the plane's speed v, then from A to B, we have a total speed of v-28. When the plane is flying from B to A, we have a total speed of v+28.

Let's form our two equations:

1. A to B: distance = total speed * time -> d=(v-28)*4 or d=4(v-28) (equation 1)
2. B to A: distance = total speed * time -> d=(v+28)*3.5 or d=3.5(v+28) (equation 2)

We can solve in a number of ways... In this case, we can eliminate our d variable by dividing: eq1/eq2

1. equation1/equation2 -> [d=4(v-28)] / [d=3.5(v+28)] -> d/d= [4(v-28)] / [3.5(v+28)]
2. since d/d is 1, we can multiple both sides by 3.5(v+28) to get: 4(v-28)=3.5(v+28)
3. distribute the 4 and 3.5 on each side: 4v-112=3.5v+98
4. collect like terms and solve for v: .5v = 210 -> v=420 mi/hr

And you're done!

Bonus: Now that you know the speed of the plane, v, you could find the distance between A and B by plugging in v=420 mi/hr into either equation 1 or equation 2.