SOLUTION: Two boats left an island at the same time to return to their home port. Their average speeds differ by 4MPH. The faster boat reachers the port after 3hpurs. The slower boat took th
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Question 336753: Two boats left an island at the same time to return to their home port. Their average speeds differ by 4MPH. The faster boat reachers the port after 3hpurs. The slower boat took thirty minutes longer. Find the speed of each boat. Found 2 solutions by nerdybill, nyc_function:Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! Two boats left an island at the same time to return to their home port. Their average speeds differ by 4MPH. The faster boat reachers the port after 3hpurs. The slower boat took thirty minutes longer. Find the speed of each boat.
.
Apply the "distance formula"
d = rt
where
d is distance traveled
r is rate or speed
t is time
.
"d" for both boats will be the same.
"30 minutes" = .5 hours
.
Let x = speed of slower boat
then
x+4 = speed of faster boat
.
4 hours = time of faster boat
4+.5 = 4.5 hours = time of slower boat
.
Distance traveled by slower boat:
4.5x
.
Distance traveled by faster boat:
4(x+4)
.
Since the went the same distance, set them equal to each other:
4.5x = 4(x+4)
4.5x = 4x+16
.5x = 16
x = 32 mph (slower boats speed)
.
Faster boats speed:
x+4 = 32+4 = 36 mph
You can put this solution on YOUR website! Fast Boat:
rate = x - 4
time = 3
Slow Boat:
rate = x
NOTE: Time is measure in hours not minutes.
So, 30 minutes = 30/60 = 1/2 = 0.5.
The slow boat took 0.5 longer to reach the port. This means the time for the slow boat is 3 hours + 0.5 or 3.5 hours.
Distances are equal because they are going to the same location leaving the same Island.
Here is your equation:
3(x + 4) = 3.5x
Can you find x now and then proceed to find the speed of each boat?
HINT: Look above for the rate of each boat after finding the value of x.
