Please help

[Ialwaysneedhelp111]

Two ferries run by Irish Ferries leave every day from Dublin Port to Holyhead by exactly the same route. The distance of the trip is 148 km. The average speed of the Jonathan Swift is 34 km/h greater than the average speed of the slower Ulysses ferry. As a result, the Jonathan Swift arrives 1 hour 42 minutes ahead of the Ulysses. Find the average speed of each ferry. This is what I have is far but I don’t think it’s correct. The answers are 74 km/h and 40 km/h

 

[Romsek]

It will be to your advantage to learn to use meaningful variable names.

\(\displaystyle s_u = s_s+34\\
\dfrac{148}{s_s} = \dfrac{148}{s_u} + \dfrac{17}{10}\\
\dfrac{148}{s_s} = \dfrac{148}{s_s+34} + \dfrac{17}{10}\\

148\left(\dfrac{1}{s_s} - \dfrac{1}{s_s+34}\right) = \dfrac{17}{10}\\

\dfrac{s_s+34 - s_s }{s_s(s_s+34)}= \dfrac{17}{1480}\\

50320 = 17s^2 + 578s\\

s^2 + 34s - 2960 = 0\\

s = \dfrac{-34 \pm \sqrt{34^2 + 4(2960)}}{2}\\

s = (40, -74)\\

\text{and as speed is non-negative}\\
s=40~km/hr
\)

 

[Dr.Peterson]

You have apparently defined x as the speed of the Ulysses, and y as the speed of the Swift. (It would be a very good idea to state that.)

Your equation is [MATH]\frac{148}{x} - \frac{148}{y} = y + 1.7[/MATH]. But what does this mean? The first term is the time taken by the Ulysses, and the second is the time taken by the Swift. So your left-hand side is the difference in the times.

So why is your right side the sum of the speed of the Swift and the extra time it takes? You can't add a speed and a time. It should just be 1.7 (hours).

It's a good idea never to start solving until you are sure your equation is right; a way to check that is to imagine you are explaining the reason for each piece, including the units involved.

 

[Steven G]

Always check to see if the units are correct, as mentioned by Dr Peterson.