Question

Two canoes travel down a river, starting at 9:00 a.M. One canoe travels twice as fast as the other. After 4.5 hours, the canoes are 11.25 miles apart. What is the speed of each canoe?

Answer 1

Answer:

$v_1=3.33 \ miles/hour\\v_2=6.66 \ miles/hour$

Step-by-step explanation:

Constant Speed Motion

When the object travels the same distances in the same period of time, the speed is constant and is can be calculated as

$\displaystyle v=\frac{x}{t}$

where x is the distance and t is the time

There are two canoes traveling at speeds v1 and v2. One of them has twice the speed as the other. Let's say

$v_2=2v_1$

When t hours have passed, the canoes have traveled x1 and x2 respectively.

$x_1=v_1t$

$x_2=v_2t$

Since

$v_2=2v_1$

Then

$x_2=2v_1t$

The distance between them is

$X=x_2-x_1=2v_1t-v_1t$

$X=v_1t$

That distance is known and equals 11.25 miles, thus

$v_1t=15$

Solving for v1 and using t=4.5 hours

$\displaystyle v_1=\frac{15}{4.5}$

$v_1=3.33 \ miles/hour$

$v_2=2\times 3.33$

$\boxed{v_2=6.66 \ miles/hour}$