determine the approx. speed of each motorcycle

Question

brandy dawson and jason dodge start a motorcycle tip at the same point. both are traveling to san antonio a distance of about 400 kilometers. brandy rides 30 kilometers per hour faster than jason does. when brandy reaches her destination, jason has only traveled to austin, texas a distance of about 250 kilometers. determine the approx. speed of each motorcycle?

 

identify the variables, write the equation and solve algebraically 

Answer 1

Jason travels at speed v over a time t and reaches a distance of 250 km.

Brandy travels at speed v+30 kph over the same time t and reaches a distance of 400 km.

 

distance = speed * time

 

Jason:  250 = vt

Brandy:  400 = (v+30)t

 

Note we have 2 equations in 2 unknowns v and t.  Get t from the first equation and plug it into second equation:

 

t = 250/v

400 = (v+30)(250/v)

 

Now solve for v from this last equation.  Multiply both sided by v:

 

400v = (v+30)(250) = 250v + 7500

150v = 7500

v = 7500/150 kph = 50 kph

 

Jason travels at 50 kph.  Brandy travels at 50+30 = 80 kph.