SOLUTION: Jim began a ​206-mile bicycle trip to build up stamina for a triathlete competition.​ Unfortunately, his bicycle chain​ broke, so he finished the trip walking. The whole trip

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Question 1164424: Jim began a ​206-mile bicycle trip to build up stamina for a triathlete competition.​ Unfortunately, his bicycle chain​ broke, so he finished the trip walking. The whole trip took 6 hours. If Jim walks at a rate of 5 miles per hour and rides at 37 miles per​ hour, find the amount of time he spent on the bicycle.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
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.




Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Jim began a ​206-mile bicycle trip to build up stamina for a triathlete competition.​ Unfortunately, his bicycle chain​ broke, so he finished the trip walking. The whole trip took 6 hours. If Jim walks at a rate of 5 miles per hour and rides at 37 miles per​ hour, find the amount of time he spent on the bicycle.
Let time spent riding be T

Then time spent walking was, 6 - T

We then  get the following DISTANCE equation: 37T + 5(6 - T) = 206

37T + 30 - 5T = 206

37T - 5T = 206 - 30

32T = 176

Time spent riding, or  

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