Applications of system of equations: word problems

Question

you and a friend share the driving on a 280 mile trip. your average speed is 58 miles per hour. your friend's average speed is 53 miles per hour .you drive one hour longer than your friend. how many hours did each of you drive ?

Answer 1

The average speed is defined as the ratio of distance traveled over time traveled. Two distances friend's and mine add up to 280 miles.

S_me+S_friend=280

V_me*t_me +V_friend*t_friend = 280 substitute either t_me = t_friend+1 or t_friend = t_me-1

58*t_me+53*(t_me-1) = 280

111*t_me = 280+53 = 333 => t_me = 3 hours.

My time 3 hours, friend's time 2 hours.

Answer 2

d=rt

distance = rate of speed times time

280 = 58(x) + 53(x+1), solve for x

then add one for your friend's time

280 = 58x + 53x + 53

111x = 280-53 = 227

x = 227/111, a little over 2 hours

x+1 = 338/111, a little over 3 hours