SOLUTION: Jim and Mateo live across a lake from each other at a distance of about 3 miles. Jim can row his boat to Mateo's house in 1 hour and 20 minutes. Mateo can drive his motorboat the s

Algebra ->  Radicals -> SOLUTION: Jim and Mateo live across a lake from each other at a distance of about 3 miles. Jim can row his boat to Mateo's house in 1 hour and 20 minutes. Mateo can drive his motorboat the s      Log On


   

Question 1035510: Jim and Mateo live across a lake from each other at a distance of about 3 miles. Jim can row his boat to Mateo's house in 1 hour and 20 minutes. Mateo can drive his motorboat the same distance in 30 minutes.
If they leave their house at the same time and head toward each other, how long will it be before they meet?
How far from the nearest shore will they be when they meet?
Answer by ikleyn(52770) About Me  (Show Source):
You can put this solution on YOUR website!
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Jim and Mateo live across a lake from each other at a distance of about 3 miles. Jim can row his boat to Mateo's house
in 1 hour and 20 minutes. Mateo can drive his motorboat the same distance in 30 minutes.
If they leave their house at the same time and head toward each other, how long will it be before they meet?
How far from the nearest shore will they be when they meet?
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%283%2F%28%284%2F3%29%29%29%2At+%2B+%283%2F0.5%29%2At = 3.    (1) ( <<<--- 4%2F3 = 4%2F3 of an hour = 1 hour and 20 minutes )


Comments:

   3%2F%28%284%2F3%29%29 is the Jim's rate (speed).

   3%2F0.5 is the Mateo's rate (speed).

   (1) is the standard Travel and Distance equation.


Solution


Simplify (1): 

%289%2F4%29%2At+%2B+6t = 3,

multiply both sides by 4:

9t + 24t = 12,

33t = 12,

t = 12%2F33 = 4%2F11 of an hour.

To answer the second question, compare the values 

%283%2F%28%284%2F3%29%29%29%2A%284%2F11%29   and   %283%2F0.5%29%2A%284%2F11%29,

that are the distances covered by Jim and Mateo respectively.

Solved.