SOLUTION: 1- a six passanger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind then what is the

Click here to see ALL problems on Miscellaneous Word Problems

Question 66725: 1- a six passanger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind then what is the wind speed?

2- Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour than Smith's. How fast was each one traveling ?
Found 2 solutions by Nate, ankor@dixie-net.com:
Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!
1- a six passanger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind then what is the wind speed?
With Wind:
rate = 180 + x
time = t
distance = 7
distance/rate = time
With Wind: 7/(180 + x) = t
Against Wind:
rate = 180 - x
time = t
distance = 5
distance/rate = time
Against Wind: 5/(180 - x) = t
t = t
7/(180 + x) = 5/(180 - x)
7(180 - x) = 5(180 + x)
1260 - 7x = 900 + 5x
360 = 12x
30 = x
The wind was 30mph.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2- Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour longer than Smith's. How fast was each one traveling ?
Smith:
rate = r
time = t
distance = 45
distance/time = rate
45/t = r
Jone:
rate = r + 5
time = t + 1.5
distance = 70
distance/time = rate
70/(t + 1.5) = r + 5
70/(t + 1.5) - 5 = r
r = r
45/t = 70/(t + 1.5) - 5

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
1- a six passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind. in the same amount of time as it flies 5 miles against the wind, then what is the wind speed?
:
Let x = wind speed:
;
Speed against the wind = (180-x)
Speed with the wind = (180+x)
:
Write a time equation: time = dist/speed
:
=
:
Cross multiply and you have:
5(180+x) = 7(180-x)
;
900 + 5x = 1260 - 7x
5x + 7x = 1260 - 900
12x = 360
x = 360-12
x = 30 mph speed of the wind:
:
:
Check: 5/150 = 7/210
:
:
:
2- Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour than Smith's. How fast was each one traveling ?
:
I understand this to mean:
Jones' 70 mi trip took a half hr longer than Smith's 45 mi trip
:
Let Smith's speed = s
Then Jones' speed = (s+5)
:
Write a time equation again:
:
Smith's time + .5 hr = Jones' time
=
:
Get rid of the denominators by multiplying equation by 2s(s+5), you then have:
45(2(s+5)) + s(s+5) = 70(2s)
;
90s + 450 + s^2 + 5s = 140s
:
s^2 + 90s + 5s - 140s + 450 = 0
:
s^2 - 45s + 450 = 0
:
This quadratic equation will factor to:
(s-30)(s-15) = 0
:
s = 30 mph or s = 15 mph
:
Both solutions will work, however, practically the bike av speed would be:
Smith: 15 mph and Jones: 20 mph, I would think
:
:
Check:
Jones time - Smiths time
70/20 - 45/15 =
3.5 hr - 3 hr = 1/2 hr