MHB I just want to know one divergent formula

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    Divergent Formula
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SUMMARY

This discussion centers on a mathematical problem involving two trains, A and B, departing simultaneously from the same point, with speeds of 60 mph and 75 mph, respectively. It concludes that Train B, traveling at 75 mph, cannot reach a point where it has traveled twice the distance of Train A, which travels at 60 mph. The relationship between their speeds indicates that Train B is always 5/4 times the distance of Train A, confirming that there is no time \( t > 0 \) where this condition is satisfied. The relevant formula used in the analysis is \( d = st \), where \( d \) represents distance, \( s \) speed, and \( t \) time.

PREREQUISITES
  • Understanding of basic algebra and distance-speed-time relationships
  • Familiarity with the formula \( d = st \)
  • Knowledge of ratios and proportions in speed
  • Basic problem-solving skills in mathematics
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  • Study the concept of ratios in speed and distance calculations
  • Explore algebraic manipulation techniques for solving equations
  • Learn about relative motion problems in physics
  • Practice similar problems involving multiple objects moving at different speeds
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This discussion is beneficial for students studying algebra, educators teaching mathematical concepts, and anyone interested in understanding relative motion and speed calculations in physics.

justone
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Hello. I asked my professor and he couldn't figure it out. If train A and B leave the same point at the same time, A traveling 60mph, B traveling 75mph, how long will it take for B to have traveled twice as far as A?
 
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justone said:
Hello. I asked my professor and he couldn't figure it out. If train A and B leave the same point at the same time, A traveling 60mph, B traveling 75mph, how long will it take for B to have traveled twice as far as A?

Train B is traveling 5/4 as fast as train A. If they depart at the same time, then train B will always have traveled 5/4 as far as train B...there is no point in time (where $0<t$) for which train B will have traveled twice as far as train A.

I am going to move this thread to our algebra forum, as that is a better fit.
 
Recall that $d=st$, where $d$ is distance, $s$ is speed and $t$ is time.

With the speeds of train A and train B denoted as $s_1$ and $s_2$ respectively, we must have

$s_2t=2s_1t\implies s_2=2s_1$, but this is clearly not true.
 

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