SOLUTION: To deliver a package, a messenger must travel at a speed of 60 miles per hour on land and then use a motorboat whose speed is 20 miles per hour in still water. The messenger goes b

Algebra.Com
Question 322397: To deliver a package, a messenger must travel at a speed of 60 miles per hour on land and then use a motorboat whose speed is 20 miles per hour in still water. The messenger goes by land to a dock and then travels on a river against a current of 4 miles per hour. He reaches his 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 solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Everything in this problem is based on the distance equals rate times time formula.

Let represent the distance traveled on land.

Let represent the distance traveled on the water.

Let represent the elapsed time traveling on land.

We know the rate of speed on land because that is given as 60 mph.

The rate of speed for the outbound trip on water is the rate in still water MINUS the rate of the current (because he was traveling AGAINST the current), so 20 mph minus 4 mph is 16 mph.

Likewise, the rate of speed for the return trip on water is 24 mph.

If the total outbound trip took 4.5 hours and the land part of the trip took hours, then the water part of the outbound trip must have taken hours.

Similarly, the water part of the return trip must have taken hours.

Let's put some of this together. We can describe the outbound trip over water by the relationship:



And we can describe the return trip over water as:



Having two things both equal to , we can set them equal to each other:



From which we can solve for hours, the travel time on land. (Verification of this result is left as an exercise for the student).

Then, knowing that , we can say that

Further, says that the travel time for the outbound trip on water is , hence the distance over water for the outbound trip is miles.

As a check, the distance over water for the return trip better be the same as for the outbound trip:



And our answer checks.

John
RELATED QUESTIONS

To deliver a package, a messenger must travel at a speed of 60mi/h on land and then use a (answered by ankor@dixie-net.com)
I am having difficulty setting up the equation for this problem. Thank you for any help. (answered by ptaylor)
to deliver a package a messenger must travel at a speed of 60mi/h on land and then use a... (answered by Greenfinch)
A bike messenger rode 4.5 miles to pick up a package at the edge of town. She then rode... (answered by nyc_function)
1. A motorboat went 70 miles in 4 hours when traveling at full speed upstream on a river... (answered by ewatrrr)
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)
3. A bike messenger rode 4.5 miles to pick up a package at the edge of town. She then... (answered by JimboP1977)
A motorboat heads upstream a distance of 24 miles on a river whose current is running at... (answered by ankor@dixie-net.com)