It takes a boat ten hours to travel 100 miles down a river a

It takes a boat ten hours to travel 100 miles down a river and 15 hours to return upstream to its starting point. What is the rate of the current in the stream? It takes a private airplane 8.75 hours to make the 2400-mile trip from Washington. DC to San Francisco, CA and 5 hours to make the return trip. Assuming that the wind blows at a constant rate from San Francisco to Washington, find the airspeed of the plane and the wind rate.

Solution

14)
Speed of boat in still water = x
Speed of current = y

Upstream :
Distance = 100 miles
Time = 15 hrs
Speed = x - y
So, x - y = 100/15
x - y = 20/3 ---> equation 1

Downstream :
Distance = 100
Time = 10
Speed = x + y
so, x + y = 100/10
x + y = 10 ---> equation 2

Now, the 2 eqns are :
x - y = 20/3
x + y = 10

Adding :
2x = 20/3 + 10
2x = 50/3
x = 25/3

x + y = 10
y = 10 - 25/3
y = 5/3

So, speed of current = 5 / 3 miles per hr -----> ANSWER

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15)
Speed of plane in still air = x
Speed of wind = y

With wind :
Distance = 2400
Time = 5 hrs
Speed = x + y
x + y = 2400/5
x + y = 480 ---> equation 1

Against wind :
Distance = 2400
Time = 8.75 hrs
Speed = x - y
x - y = 2400/8.75
x - y = 1920/7 ---> equation 2

From equations 1 and 2 :
x + y = 480
x - y = 1920/7

Adding :
2x = 480 + 1920/7
2x = 5280/7
x = 2640/7 mph

y = 480 - 2640/7
y = 720/7 mph

So, speed of plane = 2640/7 mph ---> ANSWER
Wind speed = 720/7 mph ---> ANSWER