Welcome to our community

Be a part of something great, join today!

[SOLVED] Velocity of a jet

dwsmith

Well-known member
Feb 1, 2012
1,673
A propeller plane and a jet travel 3000miles. The velocity of the plane is 1/3 the velocity of the jet. It takes the prop plane 10 hours longer to complete the trip. What is the velocity of the jet.

Let \(\mathbf{v} = \frac{dx}{dt}\) and \(dx = 3000\). The \(dt = t - t_0\). We can always let \(t_0 = 0\) so \(\mathbf{v}_{\text{jet}} = \frac{3000}{t_{\text{jet}}}\). It appears that the information about the prop plane is unnecessary or can I use that information to determine \(t_{\text{jet}}\)?

We know that \(\mathbf{v}_{\text{prop}} = \frac{1}{3}\mathbf{v}_{\text{jet}}\) and the time require is \(t_{\text{prop}} = t_{\text{jet}} + 10\).
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Letting the velocity of the jet be $v$ and observing that both planes travel the same distance $d$, we may write:

\(\displaystyle d=vt=\frac{v}{3}(t+10)\)

For $0<d$, we must have $0<v$, and so we may divide through by $v$ to obtain:

\(\displaystyle t=\frac{t+10}{3}\implies t=5\)

Hence:

\(\displaystyle v=\frac{d}{5}\)
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
A propeller plane and a jet travel 3000miles. The velocity of the plane is 1/3 the velocity of the jet. It takes the prop plane 10 hours longer to complete the trip. What is the velocity of the jet.

Let \(\mathbf{v} = \frac{dx}{dt}\) and \(dx = 3000\). The \(dt = t - t_0\). We can always let \(t_0 = 0\) so \(\mathbf{v}_{\text{jet}} = \frac{3000}{t_{\text{jet}}}\). It appears that the information about the prop plane is unnecessary or can I use that information to determine \(t_{\text{jet}}\)?
"[tex]v_{\text{jet}}= \frac{3000}{t_{text}}[/tex] is a formula for the speed of the jet. This problem is asking for a specific numerical answer.

We know that \(\mathbf{v}_{\text{prop}} = \frac{1}{3}\mathbf{v}_{\text{jet}}\) and the time require is \(t_{\text{prop}} = t_{\text{jet}} + 10\).
I would write, rather, that the time is [tex]\frac{3000}{v_{\text{jet}}}[/tex]. The time required for the prop plane to fly 3000 mi would be [tex]\frac{3000}{v_{\text{prop}}}[/tex][tex]= \frac{3000}{\frac{1}{3}v_{\text{jet}}}[/tex][tex]= \frac{9000}{v_{\text{jet}}}[/tex] and that is 10 hours more than the time required for the jet:
[tex]\frac{3000}{v_{\text{jet}}}[/tex][tex]= \frac{9000}{v_{\text{jet}}}- 10[/tex].

Solve that equation.
 
Last edited: