An airship propelled by some mechanical device travels five miles in ten minutes in the direction of the wind, but requires one hour to go back again to the starting point against the same wind. How long would it have taken to go the whole ten miles in a calm day without any wind? Hint: You don't have to use equations to solve this problem.
we have that
5 miles -------> 10 minutes (direction of the wind)
5 miles ------> 1 hour (against the same wind)
therefore
10 miles ------> ? (without any wind)
so
Let
x -----> speed of the wind
y -----> speed of the airship
direction of the wind
speed=d/t ------> 5/10=0.5 miles per min
against the same wind
speed=5/60=1/12 miles per min
so
x+y=0.5 ------> x=0.5-y -----> equation 1
y-x=1/12 -----> equation 2
solve the system
substitute equation 1 in equation 2
y-(0.5-y)=1/12
2y=(1/12)+1/2
2y=7/12
y=7/24=0.2917 miles per min
Find the value of x
x=(1/2)-7/24
x=5/24=0.2083 miles per min
therefore
10 miles without any wind
speed=d/t ------> t=d/speed
t=10/(7/24)
t=34.29 min