Question

A boat traveled 140 miles in 6 hours. It traveled part of the distance at 10 miles/hour and

the other part of the distance at 30 miles/hour.
How long did it travel at 10 miles/hour?
How long did it travel at 30 miles/hour?

Answer 1

The boat traveled at 10 miles per hour for 2 hours and at 30 miles per hour for 4 hours.

Explanation:

Let x be the time (in hours) that the boat traveled at 10 miles per hour, and let y be the time (in hours) that it traveled at 30 miles per hour.

We know that:

x + y = 6 (the total time the boat traveled)

We also know that the boat traveled a total distance of 140 miles, which can be expressed as:

10x + 30y = 140

We can use the first equation to solve for one of the variables in terms of the other:

y = 6 - x

Substituting this expression for y into the second equation, we get:

10x + 30(6 - x) = 140

Simplifying and solving for x, we get:

10x + 180 - 30x = 140

-20x = -40

x = 2

Therefore, the boat traveled at 10 miles per hour for 2 hours and at 30 miles per hour for 4 hours.