A cruiser travels 20 miles and a power boat travels 50 miles. The cruiser travels 6mph slower than the power boat. What's the speed of each boat?

Question

Word problems

Answer 1

It seems that your question has a part missing which I guess is boats travel 20 and 50 miles in the same time range. I denote that time as T.

 

In this case, according to your question the following constraint is closed for V1 and V2:

(A) V1 = V2 - 6

where V1 stands for cruiser's speed and V2 stands for power boat's speed.

 

Furthermore, for time T cruiser travels 20 miles with speed V1 (MPH),

whereas for the same time T power travels 50 miles with speed V2 = V1 - 6 (MPH).

which results the following proportion:

(B) 20 / 50 = V1 / V2

 

Substitute V1 in the equation B with equation A.

(C) 20 / 50 = (V2 - 6) / V2

 

Solve the equation C for V2:

50 (V2 -6) = 20 (V2) >>> 50 V2 - 300 = 20 V2 >>> 30 V2 = 300 >>> V2 = 10 (MPH) Power boat's spped

 

Solve equation A for V1, where V2 = 10:

V1 = 10 - 6 = 4 (MPH) Cruiser's speed

Answer 2

Speed is distance over time. 

 

The cruiser will have less speed that the power boat.  We can write an equation that represents this.

 

Speed of power boat - speed of cruiser = 6

 

 

(50 / x) - (20 / x) = 6

 

where x is the time for each boat.

 

 

30 / x = 6

 

30 / 6 = x

 

x = 5

 

 

Plug this value of x into each boats speed.

 

Speed of cruiser = (20 miles) / (5 hours) = 4 mph

Speed of power boat = (50 miles) / (5 hours) = 10 mph

 

 

Comparing their speeds, the cruiser is slower than the power boat by 6 mph.

 

 

 

 

 

Answer 3

Do you mean, travels those distances in the same time? 

 

Let's call the speed of the cruiser x and the speed of the power boat y.

The distance traveled by the cruiser is velocity times time, or 20=x*t.  With a touch of algebra, we get t=20/x.

In the same amount of time, the power boat travelled 50 miles.  So, 50=y*t.  This becomes t=50/y.

 

We can substitute 20/x and 50/y in place of t (addition property of equality).  Starting from

t=t, we make the substitutions on either side of the equals sign:

20/x = 50/y, or 20/x - 50/y = 0.

We also know that the cruiser is slower by 6 mph, or x = y-6.

Substituting this into the previous equation,

20/(y-6)-50/y=0.

 

Multiply both sides by y(y-6):

20y - 50(y-6) = 0.  Distribute the 50:

-30y + 300 = 0.  Subtract 300 from both sides:

-30y = -300.  Divide by -30:

y=10

 

So, the power boat is moving at 10 mph.  The cruiser is 6 mph slower, so it travels at 4 mph.