![\text{Answer: }\text{Distance traveled by steamboat}=20\text{ knots}\\\text{Distance traveled by yacht }=20+20=40\text{ knots}](https://tex.z-dn.net/?f=%5Ctext%7BAnswer%3A%20%7D%5Ctext%7BDistance%20traveled%20by%20steamboat%7D%3D20%5Ctext%7B%20knots%7D%5C%5C%5Ctext%7BDistance%20traveled%20by%20yacht%20%7D%3D20%2B20%3D40%5Ctext%7B%20knots%7D)
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}](https://tex.z-dn.net/?f=%5Ctext%7BDistance%20traveled%20by%20steamboat%7D%3D%5Ctext%7B%20Distance%20traveled%20by%20yacht%7D%5C%5C%5C%5Cx%5Ctimes%205%3D%28x%2B20%29%5Ctimes%202.5%5C%5C%5C%5C5x%3D2.5x%2B50%5C%5C%5C%5C5x-2.5x%3D50%5C%5C%5C%5C2.5x%3D50%5C%5C%5C%5Cx%3D%5Cfrac%7B50%7D%7B2.5%7D%5C%5C%5C%5Cx%3D20%5Ctext%7B%20knots%7D)
Hence,
![\text{Distance traveled by steamboat}=20\text{ knots}\\\text{Distance traveled by yacht }=20+20=40\text{ knots}](https://tex.z-dn.net/?f=%5Ctext%7BDistance%20traveled%20by%20steamboat%7D%3D20%5Ctext%7B%20knots%7D%5C%5C%5Ctext%7BDistance%20traveled%20by%20yacht%20%7D%3D20%2B20%3D40%5Ctext%7B%20knots%7D)