Question

you are traveling to an island that is accesible only by boat. you plan to take one boat there and a different boat back. You'll be traveling on the steamboat and the yacht. The steamboat makes the trip in 5 hours. The yacht makes the trip in 2.5 hours. The yacht is 20 knots faster than the steamboat. For each boat, the trip time multiplied by the speed equals the distance traveled. You know both boats will travel the same distance. How fast is each boat traveling in knots (nautical miles per hour)?

Answer 1

$\text{Answer: }\text{Distance traveled by steamboat}=20\text{ knots}\\\text{Distance traveled by yacht }=20+20=40\text{ knots}$

Step-by-step explanation:

Since we have given that

Time taken by steamboat makes the trip=5 hours

Time taken by yacht makes the trip =2.5 hours

Since we have also given that

the yacht is 20 knots faster than the steamboat,

So let the speed of steamboat be x

Let the speed of yacht be x+20

Now,  we have given that both boats will travel the same distance ,

So,

$\text{Distance traveled by steamboat}=\text{ Distance traveled by yacht}\\\\x\times 5=(x+20)\times 2.5\\\\5x=2.5x+50\\\\5x-2.5x=50\\\\2.5x=50\\\\x=\frac{50}{2.5}\\\\x=20\text{ knots}$

Hence,

$\text{Distance traveled by steamboat}=20\text{ knots}\\\text{Distance traveled by yacht }=20+20=40\text{ knots}$