Question

Traveling upstream (against the current) in a boat, you can travel 35 miles in 7 hours. It

takes half the time (3.5 hours) to travel the same distance downstream (with the
current). Find the speed of the current.

Answer 1

The speed of the current is 2.5 miles per hour

Explanation:

Systems of Equations

Let's call:

B = velocity of the boat

C = velocity of the current

When traveling upstream, the current is against the boat thus the relative velocity is B-C.

The distance is the product of the velocity by the time. Since the boat takes 7 hours to travel 35 miles upstream, thus:

d=(B-C)*7=35

Dividing by 7:

B - C = 5 [1]

When traveling downstream, the current and the boat are collaborative and the relative velocity is B+C. The travel takes now 3.5 hours, thus:

d=(B+C)*3.5=35

Dividing by 3.5:

B + C = 10 [2]

Subtracting [2] - [1]:

2C = 5

C = 5/2 = 2.5

The speed of the current is 2.5 miles per hour