SOLUTION: I refer to question number 139334 and question number 139296, both answerd by stanbon. It takes Boat A 3 hours longer to travel 50kms than it takes Boat B to travel 60kms. Boa

Question 141890: I refer to question number 139334 and question number 139296, both answerd by stanbon.

It takes Boat A 3 hours longer to travel 50kms than it takes Boat B to travel 60kms. Boat A travels one third the speed of Boat B. What is the speed of each boat.
----------------------
A-Boat DATA:
distance 50 km ; Rate = x kph ; time = 50/x
-----------------------
B-Boat DATA:
distance = 60 km ; rate = 3x kph ; time = 60/(3x)
----------------------------------
EQUATION:
time A - time B = 3
50/x - 60/(3x) = 3
Multiply thru by 3x to get
150 - 60 = 9x
90 = 9x
x = 10 kph (speed of A-Boat)
3x = 30 kph (speed of B-Boat)
==========================

It takes a cabin cruiser 3 hours longer to travel 50kms than it takes a power boat to travel 60kms. The cruiser travels one third the speed of the power boat. Find the speed of each boat.
-------------
Cruiser DATA:
distance = 50 km ; rate = x kph ; time = 50/x hrs
--------------
Power Boat DATA:
distance = 60 km ; rate = 3x kph ; time = 60/(3x) hrs
-----------------
EQUATION:
cruise time = power boat time + 3 hrs.
50/x = 60/3x + 3
--------
Multiply thru by 3x to get:
150 = 60 + 9x
210 = 9x
x = 70/3 = 23 1/3 kph (cruiser speed)
3x = 70 kph (power boat speed)
==================

The questions are identical, save for the description of the boats, yet the answers are different.
Please confirm the answer to the second question is correct ...... I would have thought the equation should have read:
Multiply thru by 3x to get:
150 = 60 + 9x
90 = 9x
x = 90/9 = 10 kph (cruiser speed)
3x = 10*3 = 30 kph (power boat speed)

Thanks
George

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=rate (speed) of Boat B
Then r/3=speed of Boat A
Time required for boat B to travel 60 km=60/r
Time required for Boat A to travel 50 km=50/(r/3)=150/r
And we are told that Boat A's time is 3 hours longer than Boat B's time, so:
150/r=(60/r)+3 multiply each term by r
150=60+3r subtract 60 from each side
150-60=60-60+3r collect like terms
90=3r divide each side by 3
r=30 km/h----------------------------------------speed of Boat B
r/3=30/3=10 km/h----------------------------------speed of Boat A
CK
50/10=60/30+3
5=2+3
5=5

Hope this helps---ptaylor
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