Question 324276
Rate*Time=Distance
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Let Vf be the speed of the freight train.
Let Vp be the speed of the passenger train.
1.{{{Vp=Vf+20}}}
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{{{Vp*T=340}}}
{{{T=340/Vp}}}
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{{{Vf*T=240}}}
{{{T=240/Vf}}}
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{{{340/Vp=240/Vf}}}
{{{340Vf=240Vp}}}
{{{Vf=(240/340)Vp=(12/17)Vp}}}
Substitute into eq. 1,
{{{Vp=(12/17)Vp+20}}}
{{{(17/17-12/17)Vp=20}}}
{{{(5/17)Vp=20}}}
{{{Vp=(17/5)20}}}
{{{Vp=68}}}mph
Then from eq. 1,
{{{Vf=68-20=48}}}mph