SOLUTION: A family vacation trip took 12 hours. Of the total distance, 4/5 was in a car and 1/5 was in a boat, and the car traveled 5 times as fast as the boat. How much more time, in hours,

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A family vacation trip took 12 hours. Of the total distance, 4/5 was in a car and 1/5 was in a boat, and the car traveled 5 times as fast as the boat. How much more time, in hours,      Log On

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Question 1149021: A family vacation trip took 12 hours. Of the total distance, 4/5 was in a car and 1/5 was in a boat, and the car traveled 5 times as fast as the boat. How much more time, in hours, was spent in the boat than in the car?
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the rate of the boat; then the rate of the car is 5x.

And let "d" be the traveled distance.


The time spent on the car was  t%5Bcar%5D = %28%284%2F5%29%2Ad%29%2F%285x%29  hours.


The time spent on the boat was  t%5Bboat%5D = %28%281%2F5%29%2Ad%29%2Fx.


The ratio  t%5Bcar%5D%2Ft%5Bboat%5D = %28%284%2F5%29%2Ad%29%2F%285x%29 : %28%281%2F5%29%2Ad%29%2Fx = 4%2F5.


Thus we need to separate 12 hours in two parts in proportion 4%2F5.


So, the parts are  12%2A%284%2F9%29 = 48%2F9 = 51%2F3 hours for the car and  12 - 51%2F3 = 62%2F3  hours for the boat.

Solved.