rate x time=job done word problems?

Question

show your work pleasee!

Carol can complete her paper route in 2 hours. When her brother Chet helps her, it takes them 75 minutes to complete the route. How long would it take Chet alone to complete the route?

Answer 1

In one minute, Carol does 1/120 of the job. Chet does1/x of the job in one minute. Together, 1/75 of the job is done in a minute ((1/120)+(1/x)=(1/75)).

1/120+1/x=1/75
(x/120x)+(120/120x)=1/75
(x+120)/120x=1/75
120x=75(x+120)
120x=75x+9000
45x=9000
x=200

Chet takes 200 minutes, or 3 hours and 20 minutes, to complete the route.

Answer 2

Carol: 2 hours = 120 minutes => 1 paper route
Carol: 1 minute = 1/120 paper route

Chet: x minutes = 1 paper route
Chet: 1 minute = 1/x paper route

Carol and Chet 1 minute = (1/120)+(1/x) paper route

Given:
Carol and Chet: 75 minutes = 1 paper route
Carol and Chet: 1 minute = 1/75

So,
(1/120)+(1/x) = 1/75
1/x = (1/75) - (1/120)
1/x = 0.005
x = 200

So chet takes 200 minutes = 3 hours and 20 minutes to complete a paper route on his own.

Answer 3

Carol's rate is (1 route) / (2 hr). The combined rate is (1 route) / (1.25 hr). Chet's rate, alone, would be (1 route) / (x hr), where x is unknown. We just need to solve 1/2 + 1/x = 1/1.25. We get 1/2 + 1/x = 4/5 ==> 0.5 + 1/x = 0.8 ==> 1/x = 0.8 - 0.5 = 0.3 ==> x = 1/0.3 = 10/3 or 3.33 hr, which is 3 hr 20 min, or 200 min.