If a canoe travels with a speed of A mph for 3 hours, and then with a speed of B mph for the rest of the journey, how long does it take to travel C miles?

Question

I don't understand where it says "and then with a speed of B mph for the rest of the journey." How long did the canoe travel for the rest of the journey?

Answer 1

The question is asking how long it takes in total for the canoe to travel C miles. We know that the canoe travels as speed A for the first 3 hours and speed B for any and all time thereafter. Since we do not know the values of A, B, or C, the answer will be an expression for C in terms of A and B.

 

A*3 + B*(t-3) = C

(A mph) * (3 hours) + (B mph) * (total time - 3 hours) = C miles

 

Rearranging and solving for t gives:

t = (C - 3*A)/B + 3

total time = [(C mph) - (3 hours) * (A mph)] / (B mph) + (3 hours)

 

For example, let A = 10 mph, B = 5 mph and C = 50 miles

t = (50 - 3*10)/5 + 3 = 7

 

With numbers, we can think this through and confirm that the answer makes sense.  In the first 3 hours at 10 mph, the canoe travels 3 * 10 = 30 miles.  This leaves 50 - 30 = 20 miles left to travel.  At 5 mph, this takes 20/5 = 4 hours.  In total, it took 3 + 4 = 7 hours for the canoe to travel 50 miles.