Jim began a 165 mile bicycle trip to build up stamina for a triathlete competition unfortunately his bike chain broke so he finished the trip walking the whole trip took seven hours of jim walks at a rate of 3 mph and rides at 35 mph find the amount of time he spent on the bicycle

Approximately 4.7 hours.

Step-by-step explanation:

He rode the bicycle for some time before it broke down and he walked the remaining distance. This means that Jim covered a total of 165 miles by riding at a speed of 35 miles per hour and walking at a speed of 3 miles per hour.

Let x = the distance covered by riding the bicycle.

Let y = the distance covered by walking.

Time = distance /speed

Time he used in riding would be x/35

Time he used in walking would be y/3

Since the entire trip took 7 hours,

x/35 + y/3 = 7

3x + 35y = 735 - - - - - - - - 1

Total miles covered is 165. Therefore,

x + y = 165 - - - - - - - - -- - -2

Substituting x = 165-y into equation 1, it becomes

3(165-y) + 35y = 735

495-3y + 35y = 735

-3y + 135y = 735-495

132y = 240

y = 240/132

y = 1.81m

x = 165 - 1.81 = 163.19

Amount of time that he spent on the bicycle will be

x/35 = 163.19/35

= 4.66

Approximately 4.7 hours.