Distance, Rate time Algebra

Question

To travel 60 miles, it takes Mary, riding a moped, 2 hours less than it takes Elaine to travel 50 miles riding a bicycl. Mary travelled 10 miles per hour faster than Elaine. Find the times and rates of both girls.

Answer 1

Distance = Rate × Time

 

Mary: 60 = (r + 10)(t - 2)

Elaine: 50 = (r)(t)

 

60 = rt + 10t - 2r - 20

50 = rt

 

r = 50/t

 

60 = 50 + 10t - 100/t - 20

 

60 = 10t + 30 - 100/t

 

0 = 10t - 30 - 100/t

 

Multiply the equation by t to get rid of t in the denominator

 

t[10t - 30 - 100/t = 0]

 

10t^2 - 30t -100 = 0

 

Factor out the common factor of 10

 

t^2 - 3t - 10 = 0

 

(t + 2)(t - 5) = 0

 

t + 2 = 0, t - 5 = 0

 

t = -2, t = 5

 

Time can not be negative, so t = 5 hours

 

Therefore r = 50/5 = 10 miles/hr

 

Those are Elaine's time and rate. You can substitute Elaine's values into Mary's equation to find the other two values.