How fast are the boats traveling ?

Question

A yacht makes the trip in 2.5 while the tall ship makes it in 10 hours. the tall ship is 30 knots slower than the yacht , for each boat the trip time multiplied by the speed is the distance traveled . how fast did each boat travel

Answer 1

Hi Haley,

Any word problem will have some unknown quantity or quantities they want you to find. Begin by defining variables for each of those quantities. I like to include the units in my definitions, too.

For this problem, let's define

x = speed of the yacht, in knots

y = speed of the tall ship, in knots.

The next step is to use the information in the problem to build equations out of those variables. How ever many variables you have to define, that is how many equations you will need to build.

In this case there are two unknowns, so we will need to build two equations. The first equation is based on the relationship "the tall ship is 30 knots slower than the yacht". In terms of our variables, this can be translated as:

y = x - 30.

In some cases, the equations will be built on direct relationships such as "the tall ship is 30 knots slower than the yacht". In other cases you may need to use a general formula to build an equation. That will be the case here. To build our second equation we need to know that for an object moving at constant speed, the relationship between the distance (d) it travels in a time (t), at a rate (that is speed, (r)) is

d = r t.

We don't know the distance traveled by the two vessels in this problem, but we do know they traveled the same distance in the given, differing times. Technically we are introducing a new variable here:

d = distance traveled in the given times, in miles (knots are nautical miles per hour)

but since the distance each vessel traveled is the same, we will see that we don't need to know its value;

d = x*2.5 hours, and d = y*10 hours, so 2.5 x = 10 y.

We have now built a system of two equations in two unknowns:

y = x - 30, and

2.5 x = 10 y.

These are both linear equations and the system may be solved using either substitution or elimination. If you need help finishing the problem from here I recommend we set up a session to discuss it, as piling on more information here about those techniques risks being counterproductive.

Answer 2

Y=2.5*t

ts=10(t-30)

I need more information to get a distance.