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

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) (Show Source): You can put this solution on YOUR website!
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
+ = 4.5
+ = 4.5
Multiply by 60*16 to get rid of the denominators
16x + 60y = 4.5(960)
16x + 60y = 4320
and
+ = 3.5
+ = 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 =
x = 90 miles on land
:
Find y using 16x + 60y = 4320
16(90) + 60y = 4320
1440 + 60y = 4320
60y = 4320 - 1440
60y = 2880
y =
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
RELATED QUESTIONS
to deliver a package a messenger must travel at a speed of 60mi/h on land and then use a... (answered by Greenfinch)

To deliver a package, a messenger must travel at a speed of 60 miles per hour on land and (answered by solver91311)

I am having difficulty setting up the equation for this problem. Thank you for any help. (answered by ptaylor)

To get to his parents' house, John must travel at a speed of 60 mph on land and then use... (answered by ankor@dixie-net.com)

To get to his parents' house, John must travel at a speed of 60 mph on land and then use... (answered by mananth,greenestamps)

A family is on a road trip and there average speed is 60mi/h they travel a total distance (answered by TimothyLamb)

Mary drove from amity to belleville at a speed of 50mi/h. On the way back, she drove at... (answered by solver91311)

I not sure how to write the equation for this one the one i did was wrong. To get to... (answered by scott8148)

A bike messenger rode 4.5 miles to pick up a package at the edge of town. She then rode... (answered by nyc_function)