Problema Solution
Amy takes half an hour longer than it takes her mother to walk 5 kilometers. But if Amy doubles her rate, she would cover the distance in one hour less than her mother. Find the speed of Amy and her mother.
Answer provided by our tutors
let
d = 5 km the distance each walks
v1 = the start rate of Amy, v1 > 0
2v1 = the doubled rate of Amy
v2 = the rate of her mother, v2 > 0
since speed = distance/time follows time = distance/speed
Amy takes half an hour longer than it takes her mother to walk 5 kilometers:
5/v1 = 0.5 + 5/v2
if Amy doubles her rate, she would cover the distance in one hour less than her mother:
5/(2v1) = 5/v2 - 1
(1/2)(5/v1) = 5/v2 - 1
plug 5/v1 = 0.5 + 5/v2 into the last equation:
(1/2)(0.5 + 5/v2) = 5/v2 - 1
by solving we find:
v2 = 2 km/h
click here to see the step by step solution of the equation:
5/v1 = 0.5 + 5/2
by solving we find:
v1 = 5/3
v1 = 1.67 km/h
click here to see the step by step solution:
Amy's speed was 1.67 km/h while her mother's speed was 2 km/h.