Question 376451
To deliver a package, a messenger must travel at a speed of 60mi/h on land
 and then use a motorboat whose speed is 20mi/h in still water.
 The messenger goes by land to a dock and then travels on a river against a current of 4mi/h.
 He reaches the destination in 4.5 hours and then returns to the starting point in 3.5 hours.
 How far did the messenger travel by land and how far by water? 
:
Let x = distance on land
Let y = distance on water
:
Write a time equation and simplify, for each trip
:
Land time + water time = total time
{{{x/60}}} + {{{y/((20-4))}}} = 4.5
{{{x/60}}} + {{{y/16}}} = 4.5
Multiply by 60*16 to get rid of the denominators
16x + 60y = 4.5(960)
16x + 60y = 4320
and
{{{x/60}}} + {{{y/((20+4))}}} = 3.5
{{{x/60}}} + {{{y/24}}} = 3.5
Multiply by 60*24 to get rid of the denominators
24x + 60y = 3.5(1440)
24x + 60y = 5040
:
Use elimination here; subtract 16x + 60y = 4320 from the above equation
24x + 60y = 5040
16x + 60y = 4320
-------------------subtraction eliminates y find x:
8x = 720
x = {{{720/8}}}
x = 90 miles on land
:
Find y using 16x + 60y = 4320
16(90) + 60y = 4320
1440 + 60y = 4320
60y = 4320 - 1440
60y = 2880
y = {{{2880/60}}}
y = 48 miles by water
:
:
Check these values in the original 1st equation
90/60 + 48/16 =
1.5 + 3 = 4.5, confirms our solutions