Question

You row a canoe x miles per hour down a river for 20 minutes. On the return trip, you travel 1 mile per hour slower. The return trip takes
30 minutes. How far did you ride the canoe in total?

Answer 1

Answer:

Total Distance = 2 miles

Step-by-step explanation:

We know D = RT where

D is distance

R is rate (speed)

T is time

First Leg:

Rate = x mph

Time = 20/60 = 1/3 hour

Hence, D = RT, Distance = x * 1/3 = x/3 miles

Second Leg:

Rate = x - 1

Time = 30/60 = 1/2 hour

Distance = (x - 1) * 1/2 = (x-1)/2

Total distance is the sum of both the legs, hence,

Total distance = $\frac{x}{3}+\frac{x-1}{2}=\frac{2x+3(x-1)}{6}=\frac{2x+3x-3}{6}=\frac{5x-3}{6}$ miles

Since both the distance are equal we can equate and solve:

$\frac{x}{3}=\frac{x-1}{2}\\2x=3x-3\\x=3$

Plugging this x = 3 into the total distance expression, we get:

$\frac{5x-3}{6}\\\frac{5(3)-3}{6}\\=2$

Total distance, 2 miles