Question

Kinda confused on this one and others like it . Show how to solve step by step?


Ryan flew from Wiley Post to Ponca City and back. Ryan maintained an average rate of 450 mph going to Ponca City and an average rate of 400 mph returning to Wiley Post. If the actual flying time for the roundtrip was 1 hour, about how far is it from Wiley Post to Ponca City? Round to nearest mile.

Answer 1

Distance = time x speed

Answer 2

\[\frac{miles}{hour}*hour \rightarrow\frac{miles}{\cancel{hour}}*\cancel{hour}=miles\]
So,
(450+400)mph*1h = 850miles

Answer 3

Let the time for the first trip be x
so the time of returning is 1-x

450x = 400 (1-x)
450x = 400 - 400x
950x = 400
x = 950/400

450 x (950/400) = 1068.75 miles

Answer 4

@agreene for different speed they have different time

Answer 5

@moneybird - I think you made a small error in your calculation for x. from the line:\[950x=400\]the next line should be:\[x=400/950\]

Answer 6

yup my mistake.
x = 400/950

450 x (400/950) = 3600/19

Answer 7

@moneybird - sorry - you also made one other error: 400+450=850 (not 950)

Answer 8

o yeah thanks for pointing that out calculation mistake haha
450 x (400/850) = 3600/17

Answer 9

For the benefit of @Cj Sade, I will try and summarise this:

t1 is the time taken to fly from Wiley Post to Ponca City at 450 mph
t2 is the time taken to fly from Ponca City to Wiley Post at 400 mph

we know the total time of the flight is 1 hour
so t1 + t2 = 1, giving:
(1) t2 = 1 - t1

now, distance = speed * time taken, so, when flying from Wiley to Ponca, the distance flown is:
(2) d = 450 * t1
and, when flying from Ponca to Wiley, the distance flown is the same, so:
(3) d = 400 * t2 = 400 * (1 - t1) from equation (1) above

we now have two equations for d - equations (2) and (3), so we can equate them to get:
450 * t1 = 400 * (1 - t1) = 400 - (400 * t1), therefore:
850 * t1 = 400
(4) t1 = 400 / 850 = 40 / 85 = 8 / 17

so finally, we can use equation (2) to work out the distance as follows:
d = 450 * t1 = 450 * 8 / 17 = 3600 / 17 = 211.77 miles (approx)