Question

Say you go kayaking over a 2 mile stretch of river. The river is flowing at a speed of 1mph. You go 2 miles upstream, and then 2 miles downstream, back to your starting point, for one round trip. How long would that round trip take if your average speed in still water is 5mph? (show all work)

Answer 1

Answer:

50 minutes

Step-by-step explanation:

we know that

The speed is equal to divide the distance by the time

Let

s ----> the speed in miles per hour

d ---> the distance in miles

t ---> the time in hours

so

$s=\frac{d}{t}$

step 1

Upstream

Find the time

we know that

The speed upstream is equal to the average speed still water minus the average speed of the river

so

$s=5-1=4\ mph$

$d=2\ mi$

substitute

$4=\frac{2}{t_1}$

solve for t_1

$t_1=\frac{2}{4}\ h$

simplify

$t_1=\frac{1}{2}\ h$

step 2

Downstream

Find the time

we know that

The speed downstream is equal to the average speed still water plus the average speed of the river

so

$s=5+1=6\ mph$

$d=2\ mi$

substitute

$6=\frac{2}{t_2}$

solve for t_2

$t_2=\frac{2}{6}\ h$

simplify

$t_2=\frac{1}{3}\ h$

step 3

Find the total time

Adds t_1 and t_2

$t=\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\ h$

Convert to minutes

Multiply by 60

$t=\frac{5}{6}(60)=50\ minutes$