what are the rates of the two bikers

Question

jill goes 10 mph faster on her scooter than jack can ride his bike. if jill travels 9 miles the same time that john travels 6 miles what are the rates of the two bikers

Answer 1

Hi Sca, let x represent the rate of Jack on his bike. Then Jill's rate will be x + 10.

 

Use the formula, D(istance) = R(ate) * T(ime), to solve this problem. We know the time is the same for both Jack and Jill.

 

Equation 1, Jill's time:

 

t_jill = d_jill / (x + 10), or 9 / (x + 10)

 

Equation 2, Jack's tme:

 

t_jack = d_jack / x, or 6 / x

 

t_jill must equal t_jack.

 

t_jill = t_jack

 

Substitute:

 

9 / (x + 10) = 6 / x

 

Cross multiply:

 

9x = 6x + 60

 

Combine terms:

 

3x = 60

 

x = 20

 

Jack's rate is 20 miles per hour.

 

Jill's rate is: 20 + 10, or 30 miles per hour.

 

Questions?