<PRE><B>Question 785417</B>
A delivery boy travels at a speed of 50 mph on land and in a boat whose speed is 25 mph in calm water.
 In delivering his message, he goes by land to boat which travels against the current of a river which flows 5 mph.
 If he reaches his destination in 6 hrs and returns in 5 hrs, how far did he travel by land and how far by water?
:
Let x = distance traveled by land
let y = distance traveled by water
;
from the the given information we know that the boat traveled 20 mph to the destination and traveled 30 mph on the return trip
:
Write a time equation for each way; time = dist/speed
{{{x/50}}} + {{{y/20}}} = 6
{{{x/50}}} + {{{y/30}}} = 5
----------------------------Subtraction eliminates x, find y
0 + {{{y/20}}} - {{{y/30}}} = 1
multiply equation by 60, cancel the denominators
3y - 2y = 60
y = 60 mi by boat
:
Find x
{{{x/50}}} + {{{60/20}}} = 6
{{{x/50}}} + 3 = 6
{{{x/50}}} = 3
multiply both sides by 50
x = 150 mi by land
:
You can check these solutions in the original time equations</PRE>