since time = distance/speed
d/18 + d/10 = 14
d = 90
5 hours out, 9 hours back = 14 total
A motorboat left a harbor and traveled to an island at an average rate of 18 knots. The average speed on the return trip was 10 knots. If the total trip took 14.0 hours, how far is the harbor from the island?
2 answers
v1 = an average velocity travel to island = 18 knopts
v2 = an average velocity on the return = 10 knots
t1 = time of travel to island
t2 = time on the return
L = Distance betwen harbor and island
t = t1 + t2 = total time of trip = 14 h
v1 = L / t1
18 = L / t1
L / t1 = 18
v2 = L / t2
10 = L / t2
L / t2 = 10
t = t1 + t2 = 14
t1 + t2 = 14 Subtract t1 to both sides
t1 + t2 - t1 = 14 - t1
t2 = 14 - t1
L / t2 = 10
L / ( 14 - t1 ) = 10
Now you must solve syatem of two equations:
L / t1 = 18
L / ( 14 - t1 ) = 10
The solutions are :
L = 90
t1 = 5
1 knot = 1 nautical mile per hour
L = 90 nautical mile
Proof :
v1 = L / t1 = 18 knots
v1 = 90 / 5 = 18 knots
t2 = 14 - t1
t2 = 14 - 5 = 9 h
v2 = L / t2 = 10 knots
v2 = 90 / 9 = 10 knots
v2 = an average velocity on the return = 10 knots
t1 = time of travel to island
t2 = time on the return
L = Distance betwen harbor and island
t = t1 + t2 = total time of trip = 14 h
v1 = L / t1
18 = L / t1
L / t1 = 18
v2 = L / t2
10 = L / t2
L / t2 = 10
t = t1 + t2 = 14
t1 + t2 = 14 Subtract t1 to both sides
t1 + t2 - t1 = 14 - t1
t2 = 14 - t1
L / t2 = 10
L / ( 14 - t1 ) = 10
Now you must solve syatem of two equations:
L / t1 = 18
L / ( 14 - t1 ) = 10
The solutions are :
L = 90
t1 = 5
1 knot = 1 nautical mile per hour
L = 90 nautical mile
Proof :
v1 = L / t1 = 18 knots
v1 = 90 / 5 = 18 knots
t2 = 14 - t1
t2 = 14 - 5 = 9 h
v2 = L / t2 = 10 knots
v2 = 90 / 9 = 10 knots
1 answer