You travel 3 miles downstream in a kayak at a speed of r miles per hour. You turn around and travel 4 miles upstream at a speed of 0.5r miles per hour. Finally, you turn around and return to your original starting point at a speed of r+1 miles per hour.
a)Write a model in simplified form for the total time t (in hours) of the trip.
b)How long does your trip take when r is 4 miles per hour?

Solution:

Given that,

Downstream:

Speed = r miles per hour

Distance = 3 miles

Time taken is given as:

Upstream:

Speed = 0.5r miles per hour

Distance = 4 miles

Therefore,

Therefore,

a)Write a model in simplified form for the total time t (in hours) of the trip

The total time taken is:

eqn 1 + eqn 2 + eqn 3

b)How long does your trip take when r is 4 miles per hour?

Substitute r = 4

Thus it takes 2.95 hours when r is 4 miles per hour

yes

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