SOLUTION: Suppose you are at a river resort and rent a motorboat for 5 hours starting at 7am. You are told that the boat will travel at 8 miles per hour upstream and 12 miles per hour return

Question 184033: Suppose you are at a river resort and rent a motorboat for 5 hours starting at 7am. You are told that the boat will travel at 8 miles per hour upstream and 12 miles per hour returning. you decide that you would like to go as far up the river as you can and still be back at noon. at what time should you turn back, and how far from the resort will you be at that time?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let t=amount of time used to travel upstream
And (5-t)= amount of time used to travel downstream
Distance travelled upstream=8*t
Distance travelled downstream=12(5-t)
And we know that the above two distances have to be equal, so:
8t=12(5-t) get rid of parens
8t=60-12t add 12t to each side
8t+12t=60-12t+12t collect like terms
20t=60
t=3 hr-----------------time travelled upstream
So, 7am + 3 hr=10am--------------time to turn back
5-t=5-3=2 hr ------------time travelled downstream
distance upstream =8*t=8*3=24 mi from resort
ANOTHER WAY:
let t=time used to travel upstream
Then 5-t=time used to travel downstream
Let d=distance travelled upstream; also distance travelled downstream as well as distance from resort when turning back
7am + t=time to turn back
t=d/8-----------------------------eq1
5-t=d/12---------------------------eq2
substitute t=d/8 from eq1 into eq2
5-d/8=d/12 multiply each term by 24
120-3d=2d add 3d to each side
5d=120
d=24 mi----------------------distance from resort when turning back
substitute d=24 into eq1
t=24/8=3 hrs----------------time used to travel upstream
7am+3=10am-------------time to turn back

Hope this helps---ptaylor
RELATED QUESTIONS
You are at a river resort and rent a motor boat (for 5 hours) at 7am. You are told that... (answered by josmiceli,greenestamps)

Suppose you are at a river resort and rent a motor boat for 5 hours starting at 7 A.M.... (answered by josmiceli)

suppose you are at a river resort and rent a motor boat for 5 hours starting at 7 am. You (answered by edjones)

At a river resort, you rent a motor boat for a sight seeing trip. You travel upstream at... (answered by lwsshak3)

The rate at which a river flows is one-third the speed of a boat in still water. If that... (answered by VFBundy,Theo,ikleyn)

Melissa wants to rent a boat and spend at most $59 . The boat costs $6 per hour, and... (answered by MathLover1)

You wish to cross a River from point A to the other side of the river, point B. You are... (answered by math_helper,ikleyn)

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

A motorboat heads upstream on a river that has a current of 3 miles per hour.The trip... (answered by josgarithmetic)