Math homework help

Question

Jim began a

178178​-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

88

hours. If Jim walks at a rate of

33

miles per hour and rides at

3131

miles per​ hour, find the amount of time he spent on the bicycle.

Answer 1

Let x = the time it took for riding the bike. Then an expression for the time it took walking is 8 - x (since total time was 8).

Using distance equals rate times time, an expression for the distance travelled on the bike is 31x (rate times time). Similarly the distance walking is 3 (8-x) .

If you add those distances together you get the total distance.

31x + 3 (8 - x) = 178

31 x + 24 - 3x = 178

28x = 154

x = 154/28 = 11/2 or 5 hours and 30 minutes.

8 - x = 5/2 or 2 hours 30 minutes.

Distance on the bike: 31 (11/2) = 341/2

Distance walking = 3(5/2) = 15/2

Total distance: 341/2 + 15/2 = 356/2 = 178 (check)