Question

Jenny, who rides a moped, takes 2 hours less to travel 60 miles than Maureen takes to travel 50 miles on her bicycle. Jenny travels 10 miles per hour faster than Maureen. (Hint: speed = distance ÷ time.)

Answer 1

Answer:

See below

Step-by-step explanation:

Givens

Jenny's Stats

t = m - 2

d = 60 miles

r = r1 + 10

Maureen's stats

d = 50 miles

t = m

r = r1

=======

60 = (r1 + 10) * (m - 2)

50 = r1 * m

m = 50/r1

60 = (r1 + 10)* (50/r1 - 2)  

60 = 50 + 500/r1 - 2r1 - 20

60 = 30 + 500/r1 - 2r1

60r1 = 30r1 + 500 - 2*r1^2

30r1 = 500 - 2r1^2

2r1^2 + 30r1 - 500

This quadratic factors into

2 (r1 - 10)(r1 + 25)

r1 = 10 mph             The 25 has no meaning.

m = 50/r1

m = 50/10

m = 5 hours

m - 2 = 3 hours.