SOLUTION: To get to his parents' house, John must travel at a speed of 60 mph on land and then use a motorboat that travels at a speed of 20 mph in still water. John goes by land to a dock a

Question 265461: To get to his parents' house, John must travel at a speed of 60 mph on land and then use a motorboat that travels at a speed of 20 mph in still water. John goes by land to a dock and then travels on a river against a current of 4 mph. He reaches his parent's home in 4.5 hours. The return trip takes him 3.5 hours. How far do his parents live from his house?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
To get to his parents' house, John must travel at a speed of 60 mph on land and then use a motorboat that travels at a speed of 20 mph in still water.
John goes by land to a dock and then travels on a river against a current of 4 mph.
He reaches his parent's home in 4.5 hours.
The return trip takes him 3.5 hours.
How far do his parents live from his house?
:
Let c = car distance
Let b = boat distance
:
Write a time equation for each way, time = dist/speed
+ = 4.5
and
+ = 3.5
:
Which is:
:
+ = 4.5; use elimination on these two equations
+ = 3.5
-----------------------------------subtraction eliminates c/60 & we have:
- = 1
Multiply by 48, results
3b - 2b = 48
b = 48 mi by boat
:
Find the time to travel 48 mi up stream
= 3 hrs
then
4.5 - 3 = 1.5 hrs by car
:
Find the distance by car:
60*1.5 = 90 mi by car
:
Total dist: 90 + 48 = 138 miles from his house to his parents house.
:
:
Check solution by finding the time on the return trip
90/60 + 48/24 =
1.5 + 2 = 3.5 hrs
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