Question

A boat travels 20 miles downstream and then 40 miles upstream at a constant speed

of 30 miles per hour. The time the boat travels upstream is 1.5 hours longer than the
time it travels downstream. What is the average speed of the current? Write and solve a
rational equation to answer the question.

Answer 1

Two equations were set up based on downstream and upstream travel, then solved simultaneously to find the average speed of the current, which is 2 mph.

Step-by-step explanation:

To find the average speed of the current, we can set up two equations based on the given information and solve for the speed of the current c. Let d represent the downstream time and u represent the upstream time.

First Equation (Downstream)

Downstream, the boat's effective speed includes the current, so it is traveling at (30 + c) mph:

Distance = Speed × Time

20 = (30 + c) × d

Second Equation (Upstream)

Upstream, the current works against the boat, so its effective speed is (30 - c) mph and the time is 1.5 hours longer than downstream:

40 = (30 - c) × (d + 1.5)

Solving the Equations

To solve for c, we can express d from the first equation and substitute it into the second equation:

d = 20 / (30 + c)

Now substitute into the second equation:

40 = (30 - c) × (20 / (30 + c) + 1.5)

Solving this equation gives us the average speed of the current, which is 2 mph.