Question 1164424
r * t = d
r = rate
t = time
d = distance


walking is at 5 miles per hour.
bicycling is at 37 miles per hour.


total distance is 206.
total time is 6 hours.


lex x = time walking and let y = time riding the bicycle.


you get:


x + y = 6
5x + 37y = 206


x + y is the total time.
5x + 37y is the total distance
in the second equation:
5 is the rate and x is the time.
37 is the rate and y is the time.


you have two equations that need to be solved simultaneously.
they are:
x + y = 6
5x + 37y = 206


multiply both sides of the first equation by 5 and leave the second equation as is to get:


5x + 5y = 30
5x + 37y = 206


subtract the first equation from the second to get:
32y = 176
solve for y to get:
y = 5.5
this makes x = .5 because x + y = 6


replace x and y with .5 and 5.5 in the original equations to get:
x + y = 6 becomes .5 + 5.5 = 6 which is true.
5x + 37y = 206 becomes 5 * .5 + 37 * 5.5 = 206 which becomes 2.5 + 203.5 = 206 which is also true.


x = .5 and y = 5.5 is confirmed to be good.
solution is that he rode the bicycle for 5.5 hours.