Algebra word problem

Question

Jim began a 206​-mile bicycle trip to build up stamina for a triathlon 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.

Answer 1

s = d / t

t = d / s

ride:

d = distance ridden

t = d/37 (given from the problem)

walk:

t = (206 - d)/5 (given from problem)

total trip time:

6 = d/37 + (206 - d)/5.

6 = 5d/185 + 37(206 - d)/185

6*185 = 5d + 37(206 - d)

1,110= 5d +7622-37d

-7622

6,522= 5d-37d --- COMBINE LIKE TERMS

-6522= -32d = 203.5

d=203.5 then from here using the formula t = d / s we can solve

t=203.41/37 = 5.5 hours

Answer 2

distance = velocity x time Let W=walking time, B=bicycling time

206 = 5W+37B W+B=6 W=6-B substitute 6-B for W

206=5(6-B)+37B = 30-5B+37B= 30+32B

206-30=32B

176 = 32B

B=176/32=5.5 hours= 5 1/2 hours on the bicycle

W=6-5.5= 1/2 hour walking

check the answers:

5.5(37)+.5(5)=203.5+2.5=206