Question 257170: My son has the following problem.Mike and Rene walked to the dock at 2 miles per hour,jumped into a boat,and motored to Dillion at 6 mph.If the total distance was 24 miles and the trip took 6 1/2 hours in all,how far did they go by boat. A.16.5 miles B.16.75 miles C.17 miles D.16.25 miles
Can you please show me how to do this correctly so I can instruct him? Thank you, Chuck.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! basic formula is rate * time = distance.
let w = distance they walked.
let b = distance they boated.
rate they walked is equal to 2 mph.
rate they boated is equal to 6 mph.
let t[w] = time they walked.
let t[b] = time they boated.
basic formula for when they walked becomes:
2 * t[w] = w
solve for time they walked to get t[w] = w/2
basic formula for when they boated becomes:
6 * t[b] = b
solve for time they boated to get t[b] = b/6
since the total time they took was 6.5 hours, and that's the sum of the time they walked and the time they boated, then the total time they took is given by the equation:
w/2 + b/6 = 6.5 (first equation)
since the total distance they traveled was 24 miles, and that's the miles they walked and the miles they boated, then the total distance they traveled is given by the equation:
w + b = 24 (second equation)
if you solve these equations simultaneously, then you will find the answer.
if we multiply the first equation by 2, we will get:
w + b/3 = 13
if we subtract the second equation from this, we will get:
w + b/3 = 13 minus:
w + b = 24 equals:
(b/3) - b = 13 - 24
this becomes:
(-2b/3) = -11
multiply both sides of this equation by 3 to get:
-2b = -33
divide both sides of this equation by -2 to get:
b = 16.5
that would be selection A.
to confirm this is correct, we finish the problem.
since w + b = 24, this means that w must equal 7.5 miles.
mike and renee walked 7.5 miles at 2 miles per hour.
they boated 16.5 miles at 6 miles per hour.
total distance they traveled is 7.5 + 16.5 = 24 miles.
since rate * time = distance leads to time = distance / rate, then the total time they took was:
7.5/2 + 16.5/6 = 3.75 hours walking + 2.75 hours boating = 6.5 hours total.
answers are confirmed to be good.
your answer is:
they went 16.5 miles by boat.
this is selection A.
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