SOLUTION: 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 t

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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?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2F60 + y%2F%28%2820-4%29%29 = 4.5
x%2F60 + y%2F16 = 4.5
Multiply by 60*16 to get rid of the denominators
16x + 60y = 4.5(960)
16x + 60y = 4320
and
x%2F60 + y%2F%28%2820%2B4%29%29 = 3.5
x%2F60 + y%2F24 = 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%2F8
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%2F60
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