CPM Homework Help : GB8I Problem 7-64

Maya and her family took a boat tour to see crocodiles while vacationing in Australia. The boat goes $8$ miles per hour in still water. The current of the river is $2$ miles per hours. The trip downstream took $1$ hours less than the return trip against the same current. Find the total distance Maya traveled.

Hint:

Define your variables; $d$ represents the distance traveled, $r$ represents the rate, and $t$ represents the time to travel upstream.
Also remember $d = rt$ .

Step 1 (distance traveled upstream):

$d=(8 − 2)t =6t$ because $t =$ time traveled upstream and her rate is equivalent to her speed minus the rivers.

Step 2 (distance traveled downstream):

$d = (8+2)(t − 1)= 10 (t − 1)$ because time is one hour less, and rate is equivalent to her speed plus the rivers.

More help:

What is true about both distances?

Step 3:

So $6t = 10\left(t − 1\right)$ , because the distance traveled is the same both ways.

Step 4:

Solve for $t$ and substitute the value back into one of the original distance equations in steps $1$ & $2$ .

Answer:

$30$ total miles, because it is $15$ miles one way ( $15 + 15 = 30$ ).